tag:blogger.com,1999:blog-30011204043656217702024-03-04T22:57:15.767-08:00Constraint ProgrammingJean-Charles Réginhttp://www.blogger.com/profile/06540516780781311246noreply@blogger.comBlogger55125tag:blogger.com,1999:blog-3001120404365621770.post-64931655047900142052013-03-04T23:50:00.001-08:002013-03-04T23:50:33.188-08:00A new thesis on global constraints for scheduling<br />
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<span style="background-color: white; color: #444444; font-family: inherit;">One of the best theses on scheduling with CP is the one of Petr Vilim available <a href="http://vilim.eu/petr/">here</a> but this new one entitled: <span style="text-align: justify;"><a href="http://tel.archives-ouvertes.fr/docs/00/79/43/23/PDF/DeClercq_A_10_2012.pdf">Cumulative scheduling with overloads : global constraints and decompositions </a>by </span>Alexis De Clercq is definitively a thesis I have to read soon (unfortunately thesis in France are written in French, but you can still read associated papers). Here is the abstract of the thesis:</span><br />
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<span style="font-family: inherit;"><i>Constraint programming is an interesting approach to solve scheduling problems. In cumulative scheduling, activities are defined by their starting date, their duration and the amount of resource necessary for their execution. The total available resource at each point in time (the capacity) is fixed. In constraint programming, the CUMULATIVE global constraint models this problem.</i></span></div>
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<span style="font-family: inherit;"><i>In several practical cases, the deadline of the project is fixed and can not be delayed. In this case, it is not always possible to find a schedule that does not lead to an overload of the resource capacity. It can be tolerated to relax the capacity constraint, in a reasonable limit, to obtain a solution.</i></span></div>
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<span style="font-family: inherit;"><i>We propose a new global constraint : the SOFTCUMULATIVE constraint that extends the CUMULATIVE constraint to handle these overloads. We illustrate its modeling power on several practical problems, and we present various filtering algorithms. In particular, we adapt the sweep and Edge-Finding algorithms to the SOTCUMULATIVE constraint. We also show that some practical problems require to impose overloads to satisfy business rules, modelled by additional constraints. We present an original filtering procedure to deal with these imposed overloads. We complete our study by an approach by decomposition. At last, we test and validate our different resolution techniques through a series of experiments.</i></span></div>
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<br />pschaushttp://www.blogger.com/profile/10578391475922351456noreply@blogger.com1tag:blogger.com,1999:blog-3001120404365621770.post-18570315758907056422013-01-24T06:24:00.000-08:002013-01-24T06:24:32.527-08:00Worm sudoku: an application for alldiff with precedences<div class="separator" style="clear: both; text-align: justify;">
<span style="font-family: Arial, Helvetica, sans-serif;"><span style="text-align: left;">If you want to introduce CP exercises to your students slightly more difficult than basic sudoku, you can try this variant: </span><a href="http://blog.tanyakhovanova.com/?cat=13" style="text-align: left;">wormsudoku</a><span style="text-align: left;"> (</span><span style="text-align: left;">It comes from the book </span><span style="background-color: white; line-height: 18px; text-align: justify;"><a href="http://www.amazon.com/gp/product/0199756562/ref=as_li_tf_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=0199756562&linkCode=as2&tag=tanyakhovanov-20">Taking Sudoku Seriously</a>).</span></span></div>
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<span style="background-color: white; line-height: 18px; text-align: justify;"><span style="font-family: Arial, Helvetica, sans-serif;">Fill in the grid so that every row, column, and block contains 1-9 exactly once. In addition, each worm must contain entries that increase from tail to head. For blue worms you must figure out yourself which end is the head.</span></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjQ-f3bpOO2K1Yi88J8V2fdAj0DlIbBiWKFlLK8vZ0maeIQOBilhTVXZwqfGfFiGolFbu8RaORgwIufYoRQoFqerz2xnCtq985mfueYRNB896twRC3KpmhZlzIO6JSJCBZa6cpDBcyGPEM/s1600/wormssudoku.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="color: black; font-family: Arial, Helvetica, sans-serif;"><img border="0" height="319" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjQ-f3bpOO2K1Yi88J8V2fdAj0DlIbBiWKFlLK8vZ0maeIQOBilhTVXZwqfGfFiGolFbu8RaORgwIufYoRQoFqerz2xnCtq985mfueYRNB896twRC3KpmhZlzIO6JSJCBZa6cpDBcyGPEM/s320/wormssudoku.jpg" width="320" /></span></a></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">Now I have a motivation to implement Alldiff with precedence ;-) :</span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">The AllDifferent Constraint with Precedences, </span><span style="font-family: Arial, Helvetica, sans-serif;"><a href="http://arxiv.org/find/cs/1/au:+Bessiere_C/0/1/0/all/0/1" style="text-decoration: none;">Christian Bessiere</a>, <a href="http://arxiv.org/find/cs/1/au:+Narodytska_N/0/1/0/all/0/1" style="text-decoration: none;">Nina Narodytska</a>, <a href="http://arxiv.org/find/cs/1/au:+Quimper_C/0/1/0/all/0/1" style="text-decoration: none;">Claude-Guy Quimper</a>, <a href="http://arxiv.org/find/cs/1/au:+Walsh_T/0/1/0/all/0/1" style="text-decoration: none;">Toby Walsh</a> (CPAIOR11).</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">Although, the alldiff with preds can only be used for horizontal/vertical/inside a block worms. </span><br />
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pschaushttp://www.blogger.com/profile/10578391475922351456noreply@blogger.com1tag:blogger.com,1999:blog-3001120404365621770.post-48555265405247296872013-01-20T05:44:00.001-08:002013-01-20T05:44:09.096-08:00Heavy tails in CP: The magic of restarts<!--[if gte mso 9]><xml>
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<br />
<div class="MsoNormal">
One of the theoretical work with a great impact in practice on
CP solving is the one on heavy tails phenomena: <o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span lang="EN-US" style="color: #1a1a1a; mso-ansi-language: EN-US; mso-bidi-font-family: Arial;">Gomes, Carla P., Bart Selman, and Henry
Kautz. "Boosting combinatorial search through randomization." <i>Proceedings
of AAAI</i>,1998.<o:p></o:p></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span lang="EN-US" style="color: #1a1a1a; mso-ansi-language: EN-US; mso-bidi-font-family: Arial;">In essence this work says:<o:p></o:p></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span lang="EN-US" style="color: #1a1a1a; mso-ansi-language: EN-US; mso-bidi-font-family: Arial;">“<i>There is a non negligible probability
of hitting a problem that required exponentially more time to solve than any
that had been encountered before</i>”.<o:p></o:p></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
I ran some experiments with <a href="https://bitbucket.org/oscarlib/oscar/">OscaR</a> on the Sport Scheduling
problem used in the paper:</div>
<div class="MsoListParagraphCxSpFirst" style="mso-list: l0 level1 lfo1; text-indent: -18.0pt;">
</div>
<ul>
<li><span style="text-indent: -18pt;">N (even) teams</span></li>
<li><span style="text-indent: -18pt;">Every two teams plays each other exactly once</span></li>
<li><span style="text-indent: -18pt;">The season last N-1 weeks</span></li>
<li><span style="text-indent: -18pt;">Every team plays one game in each week of the
season</span></li>
<li><span style="text-indent: -18pt;">There are N/2 periods and, each week, every
period is scheduled for one game</span></li>
<li><span style="text-indent: -18pt;">No team plays more than twice in the same period
over the course of the season</span></li>
</ul>
<br />
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -18.0pt;">
<o:p></o:p></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -18.0pt;">
<o:p></o:p></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -18.0pt;">
<o:p></o:p></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -18.0pt;">
<o:p></o:p></div>
<div class="MsoListParagraphCxSpLast" style="mso-list: l0 level1 lfo1; text-indent: -18.0pt;">
<o:p></o:p></div>
<div class="MsoNormal">
Here is a solution for 12 teams (N=12):<o:p></o:p></div>
<br/>
<div class="MsoNormal">
</div>
<table border="0" cellpadding="0" cellspacing="0" class="MsoNormalTable">
<tbody>
<tr style="height: 18.0pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt; width: 98.0pt;" width="98"></td>
<td style="border: solid black 1.0pt; height: 18.0pt; mso-border-alt: solid black .75pt; padding: .75pt .75pt .75pt .75pt; width: 98.0pt;" width="98"><div class="MsoNormal">
<b><span style="font-family: Arial; font-size: 10pt;">week1</span></b><span style="font-family: Arial; font-size: 10pt;"><o:p></o:p></span></div>
</td>
<td style="border: solid black 1.0pt; height: 18.0pt; mso-border-alt: solid black .75pt; padding: .75pt .75pt .75pt .75pt; width: 98.0pt;" width="98"><div class="MsoNormal">
<b><span style="font-family: Arial; font-size: 10pt;">week2</span></b><span style="font-family: Arial; font-size: 10pt;"><o:p></o:p></span></div>
</td>
<td style="border: solid black 1.0pt; height: 18.0pt; mso-border-alt: solid black .75pt; padding: .75pt .75pt .75pt .75pt; width: 98.0pt;" width="98"><div class="MsoNormal">
<b><span style="font-family: Arial; font-size: 10pt;">week3</span></b><span style="font-family: Arial; font-size: 10pt;"><o:p></o:p></span></div>
</td>
<td style="border: solid black 1.0pt; height: 18.0pt; mso-border-alt: solid black .75pt; padding: .75pt .75pt .75pt .75pt; width: 98.0pt;" width="98"><div class="MsoNormal">
<b><span style="font-family: Arial; font-size: 10pt;">week4</span></b><span style="font-family: Arial; font-size: 10pt;"><o:p></o:p></span></div>
</td>
<td style="border: solid black 1.0pt; height: 18.0pt; mso-border-alt: solid black .75pt; padding: .75pt .75pt .75pt .75pt; width: 98.0pt;" width="98"><div class="MsoNormal">
<b><span style="font-family: Arial; font-size: 10pt;">week5</span></b><span style="font-family: Arial; font-size: 10pt;"><o:p></o:p></span></div>
</td>
<td style="border: solid black 1.0pt; height: 18.0pt; mso-border-alt: solid black .75pt; padding: .75pt .75pt .75pt .75pt; width: 98.0pt;" width="98"><div class="MsoNormal">
<b><span style="font-family: Arial; font-size: 10pt;">week6</span></b><span style="font-family: Arial; font-size: 10pt;"><o:p></o:p></span></div>
</td>
<td style="border: solid black 1.0pt; height: 18.0pt; mso-border-alt: solid black .75pt; padding: .75pt .75pt .75pt .75pt; width: 98.0pt;" width="98"><div class="MsoNormal">
<b><span style="font-family: Arial; font-size: 10pt;">week7</span></b><span style="font-family: Arial; font-size: 10pt;"><o:p></o:p></span></div>
</td>
<td style="border: solid black 1.0pt; height: 18.0pt; mso-border-alt: solid black .75pt; padding: .75pt .75pt .75pt .75pt; width: 98.0pt;" width="98"><div class="MsoNormal">
<b><span style="font-family: Arial; font-size: 10pt;">week8</span></b><span style="font-family: Arial; font-size: 10pt;"><o:p></o:p></span></div>
</td>
<td style="border: solid black 1.0pt; height: 18.0pt; mso-border-alt: solid black .75pt; padding: .75pt .75pt .75pt .75pt; width: 98.0pt;" width="98"><div class="MsoNormal">
<b><span style="font-family: Arial; font-size: 10pt;">week9</span></b><span style="font-family: Arial; font-size: 10pt;"><o:p></o:p></span></div>
</td>
<td style="border: solid black 1.0pt; height: 18.0pt; mso-border-alt: solid black .75pt; padding: .75pt .75pt .75pt .75pt; width: 98.0pt;" width="98"><div class="MsoNormal">
<b><span style="font-family: Arial; font-size: 10pt;">week10</span></b><span style="font-family: Arial; font-size: 10pt;"><o:p></o:p></span></div>
</td>
<td style="border: solid black 1.0pt; height: 18.0pt; mso-border-alt: solid black .75pt; padding: .75pt .75pt .75pt .75pt; width: 98.0pt;" width="98"><div class="MsoNormal">
<b><span style="font-family: Arial; font-size: 10pt;">week11</span></b><span style="font-family: Arial; font-size: 10pt;"><o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 18.0pt; mso-yfti-irow: 1;">
<td style="border: solid black 1.0pt; height: 18.0pt; mso-border-alt: solid black .75pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<b><span style="font-family: Arial; font-size: 10pt;">period1</span></b><span style="font-family: Arial; font-size: 10pt;"><o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(5,7)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(3,7)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(0,10)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(2,8)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(1,4)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(5,9)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(2,9)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(8,11)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(1,6)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(0,6)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(3,4)<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 18.0pt; mso-yfti-irow: 2;">
<td style="border: solid black 1.0pt; height: 18.0pt; mso-border-alt: solid black .75pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<b><span style="font-family: Arial; font-size: 10pt;">period2</span></b><span style="font-family: Arial; font-size: 10pt;"><o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(3,11)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(5,8)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(4,7)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(6,7)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(0,2)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(3,10)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(1,8)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(4,10)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(5,11)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(1,9)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(2,6)<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 18.0pt; mso-yfti-irow: 3;">
<td style="border: solid black 1.0pt; height: 18.0pt; mso-border-alt: solid black .75pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<b><span style="font-family: Arial; font-size: 10pt;">period3</span></b><span style="font-family: Arial; font-size: 10pt;"><o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(1,2)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(4,6)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(5,6)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(3,9)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(8,10)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(0,4)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(0,11)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(2,5)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(9,10)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(7,11)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(7,8)<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 18.0pt; mso-yfti-irow: 4;">
<td style="border: solid black 1.0pt; height: 18.0pt; mso-border-alt: solid black .75pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<b><span style="font-family: Arial; font-size: 10pt;">period4</span></b><span style="font-family: Arial; font-size: 10pt;"><o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(4,9)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(2,10)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(8,9)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(1,10)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(6,11)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(2,11)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(4,5)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(0,7)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(0,3)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(3,8)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(1,5)<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 18.0pt; mso-yfti-irow: 5;">
<td style="border: solid black 1.0pt; height: 18.0pt; mso-border-alt: solid black .75pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<b><span style="font-family: Arial; font-size: 10pt;">period5</span></b><span style="font-family: Arial; font-size: 10pt;"><o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(0,8)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(0,1)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(2,3)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(4,11)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(7,9)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(1,7)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(3,6)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(6,9)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(4,8)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(5,10)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(10,11)<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 18.0pt; mso-yfti-irow: 6; mso-yfti-lastrow: yes;">
<td style="border: solid black 1.0pt; height: 18.0pt; mso-border-alt: solid black .75pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<b><span style="font-family: Arial; font-size: 10pt;">period6</span></b><span style="font-family: Arial; font-size: 10pt;"><o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(6,10)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(9,11)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(1,11)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(0,5)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(3,5)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(6,8)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(7,10)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(1,3)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(2,7)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(2,4)<o:p></o:p></span></div>
</td>
<td style="height: 18.0pt; padding: .75pt .75pt .75pt .75pt;"><div class="MsoNormal">
<span style="font-family: Arial; font-size: 10pt;">(0,9)<o:p></o:p></span></div>
</td>
</tr>
</tbody></table>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
<br/>
To solve this problem I use a first fail heuristic for the
variable choice (the uninstanciated one with smallest domain size) with ties
broken randomly. I choose randomly the value to instantiate. <o:p></o:p></div>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
<div class="MsoNormal">
</div>
<div class="MsoNormal">
</div>
Here is the <a href="https://bitbucket.org/oscarlib/oscar/">OscaR</a> model:
<pre class="scala" name="code">
val n = 12
val nbPeriods = n / 2
val Periods = 0 until nbPeriods
val nbTeams = n
val Teams = 0 until nbTeams
val nbWeeks = n - 1
val Weeks = 0 until nbWeeks
val Homes = 0 to 1 // 0/1 for home/away game
val cp = CPSolver()
val team = Array.tabulate(nbPeriods, nbWeeks, 2)((p, w, h) => CPVarInt(cp, 0 until nbTeams))
val game = Array.tabulate(nbPeriods, nbWeeks)((p, w) => CPVarInt(cp, 0 until (n * n - 1)))
val tuples = for (i <- Teams; j <- i + 1 until nbTeams) yield (i, j, i * nbWeeks + j - 1)
var solFound = false // will be set to true when a solution is found
cp.solve subjectTo {
// make the link between the team and game variables
for (p <- Periods; w <- Weeks) {
cp.add(table(team(p)(w)(0), team(p)(w)(1), game(p)(w), tuples))
}
// a team plays exactly one game per week
for (w <- Weeks) {
val teamw = for (p <- Periods; h <- Homes) yield team(p)(w)(h)
cp.add(allDifferent(teamw), Strong)
}
// every team plays against every other team
cp.add(allDifferent(game.flatten), Strong)
// a team can play at most twice in the same period
for (p <- Periods)
cp.add(gcc(team(p).flatten, Teams, 1, 2), Strong)
} exploration {
cp.binary(game.flatten,_.size, _.randomValue) // our randomized heuristic
solFound = true
}
cp.run(1) // let's start looking for a solution
</pre>
I executed 10 runs stopping when the solution was found: <br/><o:p></o:p></div>
<div class="MsoNormal">
</div>
<table border="0" cellpadding="0" cellspacing="0" class="MsoNormalTable">
<tbody>
<tr style="height: 14.2pt; mso-height-rule: exactly; mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td style="border: solid black 1.0pt; height: 14.2pt; mso-border-alt: solid black .75pt; mso-height-rule: exactly; padding: .75pt .75pt .75pt .75pt; width: 98.0pt;" width="98"><div class="MsoNormal">
<b><span style="font-family: Arial; font-size: 10pt;">time(s)</span></b><span style="font-family: Arial; font-size: 10pt;"><o:p></o:p></span></div>
</td>
<td style="border: solid black 1.0pt; height: 14.2pt; mso-border-alt: solid black .75pt; mso-height-rule: exactly; padding: .75pt .75pt .75pt .75pt; width: 98.0pt;" width="98"><div class="MsoNormal">
<b><span style="font-family: Arial; font-size: 10pt;">bkts</span></b><span style="font-family: Arial; font-size: 10pt;"><o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 14.2pt; mso-height-rule: exactly; mso-yfti-irow: 1;">
<td style="border: solid black 1.0pt; height: 14.2pt; mso-border-alt: solid black .75pt; mso-height-rule: exactly; padding: .75pt .75pt .75pt .75pt;"><div align="right" class="MsoNormal" style="text-align: right;">
<span style="font-family: Arial; font-size: 10pt;">82<o:p></o:p></span></div>
</td>
<td style="border: solid black 1.0pt; height: 14.2pt; mso-border-alt: solid black .75pt; mso-height-rule: exactly; padding: .75pt .75pt .75pt .75pt;"><div align="right" class="MsoNormal" style="text-align: right;">
<span style="font-family: Arial; font-size: 10pt;">117903<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 14.2pt; mso-height-rule: exactly; mso-yfti-irow: 2;">
<td style="border: solid black 1.0pt; height: 14.2pt; mso-border-alt: solid black .75pt; mso-height-rule: exactly; padding: .75pt .75pt .75pt .75pt;"><div align="right" class="MsoNormal" style="text-align: right;">
<span style="font-family: Arial; font-size: 10pt;">41<o:p></o:p></span></div>
</td>
<td style="border: solid black 1.0pt; height: 14.2pt; mso-border-alt: solid black .75pt; mso-height-rule: exactly; padding: .75pt .75pt .75pt .75pt;"><div align="right" class="MsoNormal" style="text-align: right;">
<span style="font-family: Arial; font-size: 10pt;">41548<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 14.2pt; mso-height-rule: exactly; mso-yfti-irow: 3;">
<td style="border: solid black 1.0pt; height: 14.2pt; mso-border-alt: solid black .75pt; mso-height-rule: exactly; padding: .75pt .75pt .75pt .75pt;"><div align="right" class="MsoNormal" style="text-align: right;">
<span style="font-family: Arial; font-size: 10pt;">900<o:p></o:p></span></div>
</td>
<td style="border: solid black 1.0pt; height: 14.2pt; mso-border-alt: solid black .75pt; mso-height-rule: exactly; padding: .75pt .75pt .75pt .75pt;"><div align="right" class="MsoNormal" style="text-align: right;">
<span style="font-family: Arial; font-size: 10pt;">900369<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 14.2pt; mso-height-rule: exactly; mso-yfti-irow: 4;">
<td style="border: solid black 1.0pt; height: 14.2pt; mso-border-alt: solid black .75pt; mso-height-rule: exactly; padding: .75pt .75pt .75pt .75pt;"><div align="right" class="MsoNormal" style="text-align: right;">
<span style="font-family: Arial; font-size: 10pt;">2<o:p></o:p></span></div>
</td>
<td style="border: solid black 1.0pt; height: 14.2pt; mso-border-alt: solid black .75pt; mso-height-rule: exactly; padding: .75pt .75pt .75pt .75pt;"><div align="right" class="MsoNormal" style="text-align: right;">
<span style="font-family: Arial; font-size: 10pt;">3634<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 14.2pt; mso-height-rule: exactly; mso-yfti-irow: 5;">
<td style="border: solid black 1.0pt; height: 14.2pt; mso-border-alt: solid black .75pt; mso-height-rule: exactly; padding: .75pt .75pt .75pt .75pt;"><div align="right" class="MsoNormal" style="text-align: right;">
<span style="font-family: Arial; font-size: 10pt;">6<o:p></o:p></span></div>
</td>
<td style="border: solid black 1.0pt; height: 14.2pt; mso-border-alt: solid black .75pt; mso-height-rule: exactly; padding: .75pt .75pt .75pt .75pt;"><div align="right" class="MsoNormal" style="text-align: right;">
<span style="font-family: Arial; font-size: 10pt;">8606<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 14.2pt; mso-height-rule: exactly; mso-yfti-irow: 6;">
<td style="border: solid black 1.0pt; height: 14.2pt; mso-border-alt: solid black .75pt; mso-height-rule: exactly; padding: .75pt .75pt .75pt .75pt;"><div align="right" class="MsoNormal" style="text-align: right;">
<span style="font-family: Arial; font-size: 10pt;">1<o:p></o:p></span></div>
</td>
<td style="border: solid black 1.0pt; height: 14.2pt; mso-border-alt: solid black .75pt; mso-height-rule: exactly; padding: .75pt .75pt .75pt .75pt;"><div align="right" class="MsoNormal" style="text-align: right;">
<span style="font-family: Arial; font-size: 10pt;">1749<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 14.2pt; mso-height-rule: exactly; mso-yfti-irow: 7;">
<td style="border: solid black 1.0pt; height: 14.2pt; mso-border-alt: solid black .75pt; mso-height-rule: exactly; padding: .75pt .75pt .75pt .75pt;"><div align="right" class="MsoNormal" style="text-align: right;">
<span style="font-family: Arial; font-size: 10pt;">6<o:p></o:p></span></div>
</td>
<td style="border: solid black 1.0pt; height: 14.2pt; mso-border-alt: solid black .75pt; mso-height-rule: exactly; padding: .75pt .75pt .75pt .75pt;"><div align="right" class="MsoNormal" style="text-align: right;">
<span style="font-family: Arial; font-size: 10pt;">9023<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 14.2pt; mso-height-rule: exactly; mso-yfti-irow: 8;">
<td style="border: solid black 1.0pt; height: 14.2pt; mso-border-alt: solid black .75pt; mso-height-rule: exactly; padding: .75pt .75pt .75pt .75pt;"><div align="right" class="MsoNormal" style="text-align: right;">
<span style="font-family: Arial; font-size: 10pt;">3<o:p></o:p></span></div>
</td>
<td style="border: solid black 1.0pt; height: 14.2pt; mso-border-alt: solid black .75pt; mso-height-rule: exactly; padding: .75pt .75pt .75pt .75pt;"><div align="right" class="MsoNormal" style="text-align: right;">
<span style="font-family: Arial; font-size: 10pt;">4291<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 14.2pt; mso-height-rule: exactly; mso-yfti-irow: 9;">
<td style="border: solid black 1.0pt; height: 14.2pt; mso-border-alt: solid black .75pt; mso-height-rule: exactly; padding: .75pt .75pt .75pt .75pt;"><div align="right" class="MsoNormal" style="text-align: right;">
<span style="font-family: Arial; font-size: 10pt;">674<o:p></o:p></span></div>
</td>
<td style="border: solid black 1.0pt; height: 14.2pt; mso-border-alt: solid black .75pt; mso-height-rule: exactly; padding: .75pt .75pt .75pt .75pt;"><div align="right" class="MsoNormal" style="text-align: right;">
<span style="font-family: Arial; font-size: 10pt;">1076619<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 14.2pt; mso-height-rule: exactly; mso-yfti-irow: 10; mso-yfti-lastrow: yes;">
<td style="border: solid black 1.0pt; height: 14.2pt; mso-border-alt: solid black .75pt; mso-height-rule: exactly; padding: .75pt .75pt .75pt .75pt;"><div align="right" class="MsoNormal" style="text-align: right;">
<span style="font-family: Arial; font-size: 10pt;">1<o:p></o:p></span></div>
</td>
<td style="border: solid black 1.0pt; height: 14.2pt; mso-border-alt: solid black .75pt; mso-height-rule: exactly; padding: .75pt .75pt .75pt .75pt;"><div align="right" class="MsoNormal" style="text-align: right;">
<span style="font-family: Arial; font-size: 10pt;">577<o:p></o:p></span></div>
</td>
</tr>
</tbody></table>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
<br/>
As you can see, 2 runs took significantly more time than the
others.<o:p></o:p></div>
<div class="MsoNormal">
To avoid this problem Gomes et. al suggest to cuttoff the
search (with a carefully chosen limit) and restart the search from scratch
(don’t forget that the search is randomized so each run is different) until the
solution is found.
<br>
From previous experiences I concluded that it is reasonable
to think there is a quite high chance to solve this problem within 5000
backtrack limit. Here is the modified <a href="https://bitbucket.org/oscarlib/oscar/">OscaR</a> code to start the search making restarts until a solution is found (this replaces the previous call to run(1))<o:p></o:p></div>
<pre class="scala" name="code">
var restart = 0
do {
cp.run(1, 5000) // search 1 sol with 5000 backtrack limit
restart += 1
} while (!solFound)
println("#restart:" + restart)
</pre>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
<br/>
Here is the result also giving the number of restarts before
reaching a solution: <br><o:p></o:p></div>
<div class="MsoNormal">
</div>
<table border="0" cellpadding="0" cellspacing="0" class="MsoNormalTable">
<tbody>
<tr style="height: 14.2pt; mso-height-rule: exactly; mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td style="border: solid black 1.0pt; height: 14.2pt; mso-border-alt: solid black .75pt; mso-height-rule: exactly; padding: .75pt .75pt .75pt .75pt; width: 98.0pt;" width="98"><div class="MsoNormal">
<b><span style="font-family: Arial; font-size: 10pt;">time(s)</span></b><span style="font-family: Arial; font-size: 10pt;"><o:p></o:p></span></div>
</td>
<td style="border: solid black 1.0pt; height: 14.2pt; mso-border-alt: solid black .75pt; mso-height-rule: exactly; padding: .75pt .75pt .75pt .75pt; width: 98.0pt;" width="98"><div class="MsoNormal">
<b><span style="font-family: Arial; font-size: 10pt;">#restarts</span></b><span style="font-family: Arial; font-size: 10pt;"><o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 14.2pt; mso-height-rule: exactly; mso-yfti-irow: 1;">
<td style="border: solid black 1.0pt; height: 14.2pt; mso-border-alt: solid black .75pt; mso-height-rule: exactly; padding: .75pt .75pt .75pt .75pt;"><div align="right" class="MsoNormal" style="text-align: right;">
<span style="font-family: Arial; font-size: 10pt;">9<o:p></o:p></span></div>
</td>
<td style="border: solid black 1.0pt; height: 14.2pt; mso-border-alt: solid black .75pt; mso-height-rule: exactly; padding: .75pt .75pt .75pt .75pt;"><div align="right" class="MsoNormal" style="text-align: right;">
<span style="font-family: Arial; font-size: 10pt;">3<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 14.2pt; mso-height-rule: exactly; mso-yfti-irow: 2;">
<td style="border: solid black 1.0pt; height: 14.2pt; mso-border-alt: solid black .75pt; mso-height-rule: exactly; padding: .75pt .75pt .75pt .75pt;"><div align="right" class="MsoNormal" style="text-align: right;">
<span style="font-family: Arial; font-size: 10pt;">1<o:p></o:p></span></div>
</td>
<td style="border: solid black 1.0pt; height: 14.2pt; mso-border-alt: solid black .75pt; mso-height-rule: exactly; padding: .75pt .75pt .75pt .75pt;"><div align="right" class="MsoNormal" style="text-align: right;">
<span style="font-family: Arial; font-size: 10pt;">1<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 14.2pt; mso-height-rule: exactly; mso-yfti-irow: 3;">
<td style="border: solid black 1.0pt; height: 14.2pt; mso-border-alt: solid black .75pt; mso-height-rule: exactly; padding: .75pt .75pt .75pt .75pt;"><div align="right" class="MsoNormal" style="text-align: right;">
<span style="font-family: Arial; font-size: 10pt;">4<o:p></o:p></span></div>
</td>
<td style="border: solid black 1.0pt; height: 14.2pt; mso-border-alt: solid black .75pt; mso-height-rule: exactly; padding: .75pt .75pt .75pt .75pt;"><div align="right" class="MsoNormal" style="text-align: right;">
<span style="font-family: Arial; font-size: 10pt;">2<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 14.2pt; mso-height-rule: exactly; mso-yfti-irow: 4;">
<td style="border: solid black 1.0pt; height: 14.2pt; mso-border-alt: solid black .75pt; mso-height-rule: exactly; padding: .75pt .75pt .75pt .75pt;"><div align="right" class="MsoNormal" style="text-align: right;">
<span style="font-family: Arial; font-size: 10pt;">1<o:p></o:p></span></div>
</td>
<td style="border: solid black 1.0pt; height: 14.2pt; mso-border-alt: solid black .75pt; mso-height-rule: exactly; padding: .75pt .75pt .75pt .75pt;"><div align="right" class="MsoNormal" style="text-align: right;">
<span style="font-family: Arial; font-size: 10pt;">1<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 14.2pt; mso-height-rule: exactly; mso-yfti-irow: 5;">
<td style="border: solid black 1.0pt; height: 14.2pt; mso-border-alt: solid black .75pt; mso-height-rule: exactly; padding: .75pt .75pt .75pt .75pt;"><div align="right" class="MsoNormal" style="text-align: right;">
<span style="font-family: Arial; font-size: 10pt;">1<o:p></o:p></span></div>
</td>
<td style="border: solid black 1.0pt; height: 14.2pt; mso-border-alt: solid black .75pt; mso-height-rule: exactly; padding: .75pt .75pt .75pt .75pt;"><div align="right" class="MsoNormal" style="text-align: right;">
<span style="font-family: Arial; font-size: 10pt;">1<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 14.2pt; mso-height-rule: exactly; mso-yfti-irow: 6;">
<td style="border: solid black 1.0pt; height: 14.2pt; mso-border-alt: solid black .75pt; mso-height-rule: exactly; padding: .75pt .75pt .75pt .75pt;"><div align="right" class="MsoNormal" style="text-align: right;">
<span style="font-family: Arial; font-size: 10pt;">1<o:p></o:p></span></div>
</td>
<td style="border: solid black 1.0pt; height: 14.2pt; mso-border-alt: solid black .75pt; mso-height-rule: exactly; padding: .75pt .75pt .75pt .75pt;"><div align="right" class="MsoNormal" style="text-align: right;">
<span style="font-family: Arial; font-size: 10pt;">1<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 14.2pt; mso-height-rule: exactly; mso-yfti-irow: 7;">
<td style="border: solid black 1.0pt; height: 14.2pt; mso-border-alt: solid black .75pt; mso-height-rule: exactly; padding: .75pt .75pt .75pt .75pt;"><div align="right" class="MsoNormal" style="text-align: right;">
<span style="font-family: Arial; font-size: 10pt;">1<o:p></o:p></span></div>
</td>
<td style="border: solid black 1.0pt; height: 14.2pt; mso-border-alt: solid black .75pt; mso-height-rule: exactly; padding: .75pt .75pt .75pt .75pt;"><div align="right" class="MsoNormal" style="text-align: right;">
<span style="font-family: Arial; font-size: 10pt;">1<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 14.2pt; mso-height-rule: exactly; mso-yfti-irow: 8;">
<td style="border: solid black 1.0pt; height: 14.2pt; mso-border-alt: solid black .75pt; mso-height-rule: exactly; padding: .75pt .75pt .75pt .75pt;"><div align="right" class="MsoNormal" style="text-align: right;">
<span style="font-family: Arial; font-size: 10pt;">11<o:p></o:p></span></div>
</td>
<td style="border: solid black 1.0pt; height: 14.2pt; mso-border-alt: solid black .75pt; mso-height-rule: exactly; padding: .75pt .75pt .75pt .75pt;"><div align="right" class="MsoNormal" style="text-align: right;">
<span style="font-family: Arial; font-size: 10pt;">4<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 14.2pt; mso-height-rule: exactly; mso-yfti-irow: 9;">
<td style="border: solid black 1.0pt; height: 14.2pt; mso-border-alt: solid black .75pt; mso-height-rule: exactly; padding: .75pt .75pt .75pt .75pt;"><div align="right" class="MsoNormal" style="text-align: right;">
<span style="font-family: Arial; font-size: 10pt;">1<o:p></o:p></span></div>
</td>
<td style="border: solid black 1.0pt; height: 14.2pt; mso-border-alt: solid black .75pt; mso-height-rule: exactly; padding: .75pt .75pt .75pt .75pt;"><div align="right" class="MsoNormal" style="text-align: right;">
<span style="font-family: Arial; font-size: 10pt;">1<o:p></o:p></span></div>
</td>
</tr>
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<span style="font-family: Arial; font-size: 10pt;">14<o:p></o:p></span></div>
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Looks like our few very long runs to find a solution have disappeared. Much more robust, don’t you think? This is the magic of restarts, simple but powerful!<o:p></o:p></div>
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<br />
CP (the oldest and most famous conference of the field) will
take place in Sweden this year.<br />
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<o:p></o:p></div>
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It doesn’t surprise me since they have very good research
teams working on CP there (with some Belgians as well ;-)): (<a href="http://www.it.uu.se/research/group/astra/">ASTRA group</a>, <a href="http://www.kth.se/en/ict/forskning/programvaruteknik-och-datorsystem">KTH</a>, <a href="http://www.sics.se/">SICS</a>)<o:p></o:p></div>
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Sweden has also a very good CP blogger aka <a href="http://www.hakank.org/constraint_programming_blog/">Hakank</a> (I hope the conference will invite
him because he does a lot for CP advertisement on the Web).<o:p></o:p></div>
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Sweden is also one of the countries visiting most frequently
our blog (top ten = Australia,Belgium,Canada,France,Germany,Sweden,Netherlands,Russia,
UK,US).<o:p></o:p></div>
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<br /></div>
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Don’t miss the deadline: <span lang="EN-US" style="color: #1a1a1a; mso-ansi-language: EN-US; mso-bidi-font-family: Arial; mso-bidi-font-weight: bold;">April 17, 2013</span> for abstract submission. <o:p></o:p></div>
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As it is has been the case since for a few years now, CP also
encourage submitting papers related to applications.<o:p></o:p></div>
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More info and call for application here: <span lang="EN-US"><a href="http://cp2013.a4cp.org/"><span style="color: #103cc0;">http://cp2013.a4cp.org/</span></a><span style="color: #1a1a1a;"><o:p></o:p></span></span></div>
<!--EndFragment-->pschaushttp://www.blogger.com/profile/10578391475922351456noreply@blogger.com0tag:blogger.com,1999:blog-3001120404365621770.post-72335011003149852762013-01-14T01:54:00.000-08:002013-01-14T05:58:31.990-08:00The risk of inbreeding, some CPAIOR statistics<!--[if gte mso 9]><xml>
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<span style="font-size: 11.0pt;">Following on the previous
post of Jean-Charles.<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-size: 11.0pt;">One of our reader suggested
to have a look at the <b><i>the workshop on organising worshops and conference in CS</i></b>: http://static.usenix.org/events/wowcs08/tech/<o:p></o:p></span></div>
<div class="MsoNormal">
<span lang="EN-US" style="color: #1a1a1a; font-size: 11.0pt; mso-ansi-language: EN-US; mso-bidi-font-family: Arial;">So I had a look and found a very
interesting presentation and article </span><span style="font-size: 11.0pt;">"Best
Practices for the Care and Feeding of a Program Committee, and Other Thoughts
on Conference Organization" (Fred Douglis, IBM).<o:p></o:p></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span style="font-size: 11.0pt;">On PC composition he says in
his presentation:<o:p></o:p></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span style="font-size: 11.0pt;">Avoid inbreeding, or the
appearance of it<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-size: 11.0pt;">- Overlap from year to year<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-size: 11.0pt;">- Institutional overlap<o:p></o:p></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span style="font-size: 11.0pt;">Here is the extract on this
topic from his article:<o:p></o:p></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<b><i><span style="font-size: 11.0pt;">A number of conferences have a tendency
to become rather inbred: they have a certain number of effectively permanent PC
members, and only rotate a small fraction of their PC members from year to
year. This is a bad idea.</span></i></b><i><span style="font-size: 11.0pt;"> I believe that the core USENIX conferences, such as
the annual conference and OSDI/NSDI1 are pretty good in this regard, as are
some other conferences like SOSP. Some other systems conferences retain a much
higher fraction of PC members, which I think results in a bit of tunnel vision,
focusing on the same topics each year with much the same perceptions of what
are good ideas and what are not.<o:p></o:p></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 11.0pt;">Another possible aspect of inbreeding is the number of
PC members from a particular organization or with a particular background. One
USENIX security conference included a few people from one organization, and
then the chair joined the same organization as the CFP came out, making it seem
like he had selected 1/3 of the PC from his own organization. This looked bad
to some, and while no one faults the chair for changing organizations, there
would not have been an issue of the other people didn’t overlap so much. I can
think of two other USENIX conferences that included over half the PC members
with ties to the same department as the chair. I’m sure these PCs contained
very talented people and I am not accusing them of bias; I am only suggesting
that conferences need to avoid the appearance of being cliquish.<o:p></o:p></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 11.0pt;">I think that conference organizers (such as USENIX)
should establish guidelines for the number of PC members that can overlap in
these respects, and then do a sanity check on PC lists prior to publishing the
CFP. Some overlap with previous years is important, but too much overlap is
terrible; finding that sweet spot would be a good topic for discussion at
WOWCS. (I would recommend 20-30%.) Some conferences such as USENIX ATC have an
informal policy of ensuring that a program chair serves on the PC the years
before and after they chair it, which offers very strong continuity and should
be adopted by all conferences.<o:p></o:p></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 11.0pt;">One way to bring in new blood is to look at authors
who have not previously served on the PC. When I chaired ATC’98, I took a
USENIX bibliography to identify all authors of ATC or OSDI papers in the
previous few years, then count their papers. I found a couple of people in my
own department at AT&T who had published pretty much every year but never
been on the PC ... and sure enough they both turned me down, despite my pleas
for the need for authors to play their part as reviewers.<o:p></o:p></span></i></div>
<div class="MsoNormal">
<i><span style="font-size: 11.0pt;">A corollary to my point about identifying people who
have published but not served is that I think it is, in general, a tragedy to
appoint someone to a PC who has never published at a conference, if the
conference has been around for at least a couple of iterations. Are there
people who could serve on a PC for conference X based on their experience at
conferences Y and Z? Sure. But if they haven’t published at X, they either
haven’t been submitting there (meaning they may not be that interested in the
conference and also that they may not be well calibrated to the material
normally published there) or they’ve been having submissions rejected. There
are generally enough published authors from previous conferences that these
authors should be tapped.</span></i><span style="font-size: 11.0pt;"> <o:p></o:p></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span style="font-size: 11.0pt;">I just wanted to check if one
of my favourite conferences, CPAIOR has a risk of inbreeding according to the
indicators we should look at from the paper of Fred Douglis.<o:p></o:p></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span style="font-size: 11.0pt;">Over the past 7 conference
2007->2013:<o:p></o:p></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span style="font-size: 11.0pt;">18% of the PC has been the
same for the past 8 years (counting on average 40 PC members)<o:p></o:p></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span lang="EN-US" style="font-size: 11pt;">2008: 54% of the PC common with
2007</span><span lang="EN-US" style="font-size: 11.0pt; mso-ansi-language: EN-US; mso-bidi-font-family: Monaco;"><o:p></o:p></span></div>
<div class="MsoNormal">
<span lang="EN-US" style="font-size: 11pt;">2009: 57%% of the PC common with
2008</span><span lang="EN-US" style="font-size: 11.0pt; mso-ansi-language: EN-US; mso-bidi-font-family: Monaco;"><o:p></o:p></span></div>
<div class="MsoNormal">
<span lang="EN-US" style="font-size: 11pt;">2010: 79% of the PC common with
2009</span><span lang="EN-US" style="font-size: 11.0pt; mso-ansi-language: EN-US; mso-bidi-font-family: Monaco;"><o:p></o:p></span></div>
<div class="MsoNormal">
<span lang="EN-US" style="font-size: 11pt;">2011: 46% of the PC common with
2010<o:p></o:p></span></div>
<div class="MsoNormal">
<span lang="EN-US" style="font-size: 11pt;">2012: 50% of the PC common with
2011<o:p></o:p></span></div>
<div class="MsoNormal">
<span lang="EN-US" style="font-size: 11pt;">2013: 32% </span><span style="font-size: 15px;">of the PC common with 2012</span><span style="font-size: 11pt;"> (with 22% of persons
coming from the same institution!, I've already posted a message on this)</span><br />
<span style="font-size: 11pt;"><br /></span>
<span style="font-size: 11pt;">Another stat: </span><br />
<span style="font-size: 11pt;">50% of the union of PC's of CPAIOR have been in at least 4/7 last PC.</span><br />
<span style="font-size: 11pt;">42% in at least 5/7</span><br />
<span style="font-size: 11pt;">32% in at least 6/7</span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span style="font-size: 11.0pt;">I’m afraid Fred Douglis would
say CPAIOR has a risk of inbreeding …</span></div>
<!--EndFragment--><br />
<!--EndFragment-->pschaushttp://www.blogger.com/profile/10578391475922351456noreply@blogger.com2tag:blogger.com,1999:blog-3001120404365621770.post-54494069643652499102013-01-11T11:23:00.000-08:002013-01-12T03:17:25.660-08:00A new reviewing processI totally agree with the remarks of Pierre.<br />
<br />
I would like to present a new reviewing process that I will propose for CPAIOR-14<br />
<br />
CP conferences are very special:<br />
<ul>
<li>publishing a paper in a conference is as hard (harder than?) as in a CP journal.</li>
<li>a lot of members of the program committee (PC) publish papers in the conference</li>
</ul>
The first point gives too much importance to the conference publication. Reviewers are fighting each others. Some of them are killing papers because they thing that it can increase their chance to have their own paper accepted. <br />
The second point is not really good and causes some problems. In my University, my CV has been reviewed by a Professor who is not in computer science. He/she write in the review: "we cannot count papers that are published in the conference in which the author is in the program committee". Therefore, he/she kills a huge number of my papers! I was upset! But is he/she wrong? I am not sure... When a best paper is given to a paper with an author who is in PC, I think we make a big mistake: the conference will not be well considered outside. <br />
<br />
Since publishing in the conference is hard (in order to have low acceptation rate as we like so much), people are complaining a lot about the reviews they receive. The problem is that there are right most of the time. We cannot have ultra selective conferences, if the chairmans are not doing their job very well, for instance by <strong>reading all the reviews. </strong>Unfortunately, this is not possible because there are too many submitted papers. <br />
Thus, a lot of things have been invented like:<br />
<ul>
<li>the authors may answer to the reviewer</li>
<li>a senior PC is created</li>
</ul>
I don't really understand the first idea, because the reviewer has not to answer to the answer and it does not mean that a reviewer cannot write whatever he wants. It could just give more work to the chairmans because there are more things to read.<br />
<br />
The second point is more interesting but it does not consider a big flaw in the general process:<br />
<br />
Any Professor at the university knows that two correctors will give different evaluations for the same homework. He knows that it is really difficult to have several correctors without having this issue and that we need to define very precisely how the homeworks have to be evaluated if we expect the same final score.<br />
For conferences, we have a lot a reviewers and, as if by magic, there is no problem to order, to compare and to discuss about a slight difference of scores. We like so much to use scores even if we know that it is so much difficult to evaluate in the same way the same work by two different persons! In order to help the chairman I introduced at CPAIOR-04 the notion of "confidence in the review", by thinking that it could help the chairman to classify the paper. However, it does not change the problem.<br />
<br />
In addition, it is very dangerous to use the scores today, because people use them to kill some other papers and because the chairmen do not read all the reviews. <br />
<br />
For instance, I recently received a review saying (I cite): "the proposed method is simple and elegant", then the reviewer says that the experiments are not sufficient to convince him, because he would like to see the use of the method on super computers. Roughtly, this is the review. Then it gave me :"strong reject". This is not normal. The chairman should complain about the reviewer. This is not possible to find a new method "simple and elegant", consistent for the classical benchmarks and complain about the absence hypothetical benchmarking and give a "strong reject". I have no problem with the rejection of the paper. I have a problem with the strong rejection. Since we use score this is important.<br />
<br />
So, even by creating senior committee we have not the guarantee that the members will read all the papers and the reviews. In addition we still have the issue of the quality of the evaluation. <br />
Thus, wan can we do?<br />
<br />
I propose to apply the two following rules:<br />
<ol>
<li><strong>We accept a paper when at least one reviewer wants to accept it.</strong> In this case, the reviewer has to select a box "I want to see this paper accepted". We have just to ensure that the paper is not a republication of another work. The author will have to integrate the negative comments for improving his paper, but there are not part of the decision process. Honestly, if at least one person is interesting, this is positive!</li>
<li><strong>When a reviewer reject a paper, he has to destroy it</strong>. This rule comes from Alain Colmerauer. If you keep a paper in your office it means that it is interesting, so you should accept it.</li>
</ol>
People are going to tell me: "your first rule is not reasonnable because friends are going to accept papers of other friends". Maybe, but I have three answers: a) it already happens. I can tell you that some papers are almost always reviewed by the same group of people working on the same topic.<br />
b) some people are also trying to group together as reviewers in order to kill some papers. With my method, this part will be almost useless.<br />
At least, if need we can propose another thing:<br />
<strong>the name of the reviewers having accepted a paper is made public.</strong><br />
<strong></strong><br />
With this rule I guess that the selected papers by reviewer will change...<br />
<br />
<br />
<br />
<br />Jean-Charles Réginhttp://www.blogger.com/profile/06540516780781311246noreply@blogger.com7tag:blogger.com,1999:blog-3001120404365621770.post-20569811872129216542013-01-04T02:15:00.002-08:002013-01-04T02:15:44.655-08:00My two cents to modernise conference publishing (in CP)
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<br />
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<br /></div>
<div class="MsoNormal">
The process of publishing has been the same
for a very long time: You submit your paper, you receive your (generally 3)
reviews, you are happy or not (often it
depends if your paper is accepted or not) and that's it. If you don’t know what I'm speaking
about I invite you to have a look on this hilarious blog post: <a href="http://matt.might.net/articles/peer-fortress/">http://matt.might.net/articles/peer-fortress/</a></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span lang="EN-GB">I see 3 major problems or risk with the
current reviewing process:<o:p></o:p></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoListParagraphCxSpFirst" style="mso-list: l1 level1 lfo1; text-indent: -18.0pt;">
</div>
<ol>
<li><span lang="EN-GB" style="text-indent: -18pt;">The opinion of 3 persons,
although not so bad cannot be considered statistically significant. Many
rejected papers are just submitted again and get a totally different outcome.
We call that the lottery effect ;-)</span></li>
<li><span lang="EN-GB" style="text-indent: -18pt;">The review can be a false negative.
It means the review says the paper is bad while it is not necessarily the case;
maybe (some) reviewers were acting in bad faith or just not expert enough to
understand fully the idea.</span></li>
<li><span lang="EN-GB" style="text-indent: -18pt;">The review can be a false positive.
It means the review says the paper is wonderful while it is not really outstanding. Sometimes reviewers having not thoroughly read the paper prefer to
be rather positive (note that in case of doubt I prefer this attitude). I don’t
say anything about reviewing a friend that might also happen.</span></li>
</ol>
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<span lang="EN-GB">I think social networks tools (or some inspired
of them) could greatly help to improve transparency and quality of the reviewing
process. Here are some ideas:</span></div>
<div class="MsoListParagraphCxSpFirst" style="mso-list: l0 level1 lfo2; text-indent: -18.0pt;">
</div>
<ul>
<li><span lang="EN-GB" style="text-indent: -18pt;">Why not make the reviews public
and attached to the paper on the conference website? This would force the
reviewers to write the best reviews they can. I think it is very valuable
information, why not share it with the readers?</span></li>
<li><span lang="EN-GB" style="text-indent: -18pt;">Why not allow commenting on the
reviews just like on a blog. If a reader disagree with the review or has a
different opinion he can tell it and share it with others. When I buy a book on
amazon, I first read the reviews written by the readers. Why don’t we have
similar information attached to articles?</span></li>
<li><span lang="EN-GB" style="text-indent: -18pt;">Why not add a “like” and “tweet”
button next to the paper. Today scientists are comparing themselves based on
h-index (this is something I discovered a few months when I joined academia).
You may like a paper even if you don’t cite it. I had a discussion with
Jean-Charles Régin recently about this h-index. In our field, it seems easier
to be cited when you work on applications rather than on algorithmic ideas such
as global constraint. Does it mean it has less impact? Not sure … But it’s
always nice when you start your article to cite some related applications first.
The number of “like” and “tweet” might also be interesting if scientists really
want to compare ;-) My opinion is that whatever the comparison measure is, it
will quickly become biased at some point. Before the h-index is was simply the
number of publications that mattered. Why do you think it’s not the case
anymore ;-)?</span></li>
</ul>
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<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span lang="EN-GB">Maybe having some of these ideas
implemented would make our CP conferences more fun and interactive. </span></div>
<div class="MsoNormal">
<span lang="EN-GB"><br /></span></div>
<div class="MsoNormal">
<span lang="EN-GB">I also believe it would favor collaboration between scientist. If you have a discussion with someone about a technical point, maybe new ideas will emerge which is very beneficial for our field. This is what we try to do with posters no? </span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
The day of
the conference, we could already present some information/comments published on
social networks attached to the article. I see one major problem: are today’s
reviewers ready to expose their review publicly and expose them to public
comments?</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
CP conference are well behind OR conference such has Informs on the usage of social networks. If I remember well, it was in the program of some persons recently elected at ACP so I hope it will change soon.</div>
<!--EndFragment-->pschaushttp://www.blogger.com/profile/10578391475922351456noreply@blogger.com0tag:blogger.com,1999:blog-3001120404365621770.post-89920819989012179302013-01-03T12:57:00.000-08:002013-01-03T12:57:36.090-08:00A non controversial blogWhen I created this blog I decided (under the pressure?) that it would be non controversial. I was thinking that it could be better not to cite anybody not to be against anybody even if they are stupid or wrong. I was thinking it could be better to avoid arguing. After some years and a discussion with Pierre Schaus, I think that the only result that we obtain is only a few number of messages and a blog which is boring. The discussion triggered by the latest message of Pierre is more interesting than a lot of other posts. A lot of people are more interested in being referenced or re-tweet than publishing interesting things. Thus, the web is full of cat pictures instead of much more interesting things. This is sad and this is so damn boring...<br />
<br />
Therefore, for this year I decided to change. <br />
<br />
The blog will become controversial.<br />
<br />
I hope that people will enjoy it more.<br />
<br />
En outre, je pense que les messages en français devraient être acceptés. D'une part parce que je soupçonne une grande partie des lecteurs d'être francophone, comme l'est une très grande partie de la communauté de CP (n'oublions pas qu'il y a pratiquement autant de participants aux JFPC qu'à la Conférence CP), et d'autre part parce que c'est beaucoup plus facile pour moi de m'exprimer en français. <br />
<br />
Ma bonne résolution de cette année (expression qui me prends plusieurs minutes à traduire en anglais) va donc être d'essayer de faire vivre ce blog d'une manière ou d'une autre<br />
<br />
Happy new year<br />
<br />
Bonne année à tous.<br />
<br />
Jean-Charles Réginhttp://www.blogger.com/profile/06540516780781311246noreply@blogger.com0tag:blogger.com,1999:blog-3001120404365621770.post-2303614903169467022012-12-08T02:44:00.001-08:002012-12-08T05:11:23.939-08:00The danger of unbalanced PC<!--[if gte mso 9]><xml>
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<div class="MsoNormal">
<span lang="EN-GB" style="font-family: Arial;">CPAIOR is one of
my favourite conferences because it “</span><span lang="EN-US" style="font-family: Verdana; mso-ansi-language: EN-US; mso-bidi-font-family: Verdana;">provides an
opportunity for researchers in one area to learn about techniques in the others”.</span><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div>
<div class="MsoNormal">
<span lang="EN-GB" style="font-family: Arial;">A few years ago,
Jean-Charles complained that there was no PC member from ILOG (now IBM) at
CP2008. I agree with him it was not enough considering the role this company
plays in the field. <o:p></o:p></span></div>
<div class="MsoNormal">
<span lang="EN-GB" style="font-family: Arial;">Last year at CPAIOR12,
7% of the CP members were from IBM. <o:p></o:p></span></div>
<div class="MsoNormal">
<span lang="EN-GB" style="font-family: Arial;">This year it’s
22%. I’m not sure people from IBM will complain any more ;-) <o:p></o:p></span></div>
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<br /></div>
<div class="MsoNormal">
<span lang="EN-GB" style="font-family: Arial;">Although I have
nothing against this company, I feel a bit uncomfortable with this percentage
and I can see some risk there. Let me illustrate this with <b><span style="color: red;">a tweet from LocalSolver (not IBM)</span></b>
(commercial local search solver):<o:p></o:p></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span lang="EN-US" style="color: #262626; font-family: Arial; mso-ansi-language: EN-US;">“Don't publish dedicated heuristic approaches without
having tried <a href="https://twitter.com/search?q=%23LocalSolver&src=hash"><span style="color: #56a6c8; text-decoration: none; text-underline: none;">#</span><span style="color: #0e70a5; text-decoration: none; text-underline: none;">LocalSolver</span></a>
on your combinatorial problem: your paper might be rejected!”<o:p></o:p></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span lang="EN-GB" style="font-family: Arial;">I don’t know if
this was a joke or not, but to me it illustrates perfectly the danger there is
if a same affiliation is over-represented in a PC of a conference. There are
other important players (commercial or open-source) also building nice solvers
that are not represented at all in this PC committee… (for instance localsolver
;-))<o:p></o:p></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span lang="EN-GB" style="font-family: Arial;">I don’t blame
anybody and I like the fact the people from industry are represented in PC. This
is only because I like CPAIOR that I make this remark. But I’m sure I’m not the
only one looking at the PC members composition before considering submitting a
paper and it would be really sad if people don’t submit because they feel
uncomfortable with the PC composition. <o:p></o:p></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span lang="EN-GB" style="font-family: Arial;">What do you think
should be the maximum percentage of people with a same affiliation in such a
conference? Maybe this should be written in the status of the conference?<o:p></o:p></span></div>
<!--EndFragment--><br />
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<br /></div>
<!--EndFragment-->pschaushttp://www.blogger.com/profile/10578391475922351456noreply@blogger.com8tag:blogger.com,1999:blog-3001120404365621770.post-36464752514939418752012-08-25T09:02:00.000-07:002012-09-01T04:39:32.602-07:00Benchmarking of CPUs: the importance of the number of memory channelsI am involved in a project aiming at improving the resolution of CP problems by using massive parallelism.<br />
Thus, I learnt parallelism like a novice. <br />
First, I thought that it was not complex to use at the same time all the cores of a modern multicore CPU. Then, I learnt that it is not so easy ...<br />
My first test was about a simple problem requiring a lot of memory (about 500Mo). I was thinking that I could run the problem 4 times at the same moment on a 4 cores machine without any problem, that is it would not need more time than with one core (or a little bit more due to the frequency change). The first result was clear : NO, it does not work like that.<br />
Thus, I made some experiments using different machines. I learnt that the results may be quite different! I reproduce the results here:<br />
Using k threads means that I try to solve the very same problem k times in parallel (one per thread). The ms column corresponds to the number of ms that are elapsed for solving all the problems (that is the time for all the threads to finish)<br />
<br />
<br />
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<td nowrap="" style="background-color: transparent; border-color: windowtext rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: solid none none solid; border-width: 1pt 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
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<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">Intel i7 920<o:p></o:p></span></div>
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<td nowrap="" style="background-color: transparent; border-color: windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: solid none none; border-width: 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
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<td nowrap="" style="background-color: transparent; border-color: windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: solid none none; border-width: 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
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<td nowrap="" style="background-color: transparent; border-color: windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: solid none none; border-width: 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
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<td colspan="2" nowrap="" style="background-color: transparent; border-color: windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: solid none none; border-width: 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 120pt;" valign="bottom" width="160"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">Intel i7 3820<o:p></o:p></span></div>
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<td nowrap="" style="background-color: transparent; border-color: windowtext windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: solid solid none none; border-width: 1pt 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
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<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
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<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">4 cœurs<o:p></o:p></span></div>
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<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">2 canaux mémoire<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"></td>
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<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">4 cœurs<o:p></o:p></span></div>
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<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">4 canaux mémoire<o:p></o:p></span></div>
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<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
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<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">2,66 Ghz<o:p></o:p></span></div>
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<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">2 threads / cœur<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"></td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">3,6 Ghz<o:p></o:p></span></div>
</td>
<td colspan="2" nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) black rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 130.85pt;" valign="bottom" width="174"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">2 threads / cœur<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 3;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">#threads<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">ms<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">perf/thread<o:p></o:p></span></div>
</td>
<td colspan="2" nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 120pt;" valign="bottom" width="160"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">ratio / 1 thread<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">ms<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 70.85pt;" valign="bottom" width="94"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">perf/thread<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 4;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">835<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">835<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1,0<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"></td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">680<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 70.85pt;" valign="bottom" width="94"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">680<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1,0<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 5;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">2<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1000<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">500<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1,7<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"></td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">750<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 70.85pt;" valign="bottom" width="94"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">375<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1,8<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 6;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">4<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1365<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">341<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">2,4<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"></td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">915<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 70.85pt;" valign="bottom" width="94"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">229<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">3,0<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 7;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">6<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1900<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">317<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">2,6<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"></td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1220<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 70.85pt;" valign="bottom" width="94"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">203<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">3,3<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 8;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">8<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: red; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">2460<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: red; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">308<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: red; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">2,7<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"></td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1530<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 70.85pt;" valign="bottom" width="94"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">191<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">3,6<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 9;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">10<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">3240<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">324<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">2,6<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"></td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1970<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 70.85pt;" valign="bottom" width="94"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">197<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">3,5<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15.75pt; mso-yfti-irow: 10; mso-yfti-lastrow: yes;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) windowtext windowtext; border-style: none none solid solid; border-width: 0px 0px 1pt 1pt; height: 15.75pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">12<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none solid; border-width: 0px 0px 1pt; height: 15.75pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">3850<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none solid; border-width: 0px 0px 1pt; height: 15.75pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">321<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none solid; border-width: 0px 0px 1pt; height: 15.75pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">2,6<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none solid; border-width: 0px 0px 1pt; height: 15.75pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none solid; border-width: 0px 0px 1pt; height: 15.75pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: red; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">2250<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none solid; border-width: 0px 0px 1pt; height: 15.75pt; padding: 0cm 3.5pt; width: 70.85pt;" valign="bottom" width="94"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: red; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">188<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext windowtext rgb(0, 0, 0); border-style: none solid solid none; border-width: 0px 1pt 1pt 0px; height: 15.75pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: red; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">3,6<o:p></o:p></span></div>
</td>
</tr>
</tbody></table>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Arial","sans-serif";"><o:p> </o:p></span></div>
<br />
<table border="0" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; height: 224px; margin: auto auto auto 2.75pt; mso-padding-alt: 0cm 3.5pt 0cm 3.5pt; mso-yfti-tbllook: 1184; width: 581px;">
<tbody>
<tr style="height: 15pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td nowrap="" style="background-color: transparent; border-color: windowtext rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: solid none none solid; border-width: 1pt 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
<td colspan="2" nowrap="" style="background-color: transparent; border-color: windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: solid none none; border-width: 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 120pt;" valign="bottom" width="160"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">Intel i7 3930<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: solid none none; border-width: 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: solid none none; border-width: 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
<td colspan="2" nowrap="" style="background-color: transparent; border-color: windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: solid none none; border-width: 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 120pt;" valign="bottom" width="160"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">AMD FX8150<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: windowtext windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: solid solid none none; border-width: 1pt 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 1;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">6 cœurs<o:p></o:p></span></div>
</td>
<td colspan="2" nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 130.85pt;" valign="bottom" width="174"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">4 canaux mémoire<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"></td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">8 cœurs<o:p></o:p></span></div>
</td>
<td colspan="2" nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) black rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 130.85pt;" valign="bottom" width="174"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">2 canaux mémoire<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 2;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">3,2 Ghz<o:p></o:p></span></div>
</td>
<td colspan="2" nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 130.85pt;" valign="bottom" width="174"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">2 threads / cœur<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"></td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">3,6 Ghz<o:p></o:p></span></div>
</td>
<td colspan="2" nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) black rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 130.85pt;" valign="bottom" width="174"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1 thread/cœur<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 3;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">#threads<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">ms<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 70.85pt;" valign="bottom" width="94"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">perf/thread<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"></td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"></td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">ms<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 70.85pt;" valign="bottom" width="94"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">perf/thread<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 4;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">715<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 70.85pt;" valign="bottom" width="94"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">715<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1,0<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"></td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">757<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 70.85pt;" valign="bottom" width="94"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">757<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1,0<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 5;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">2<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">790<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 70.85pt;" valign="bottom" width="94"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">395<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1,8<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"></td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1100<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 70.85pt;" valign="bottom" width="94"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">550<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1,4<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 6;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">4<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">900<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 70.85pt;" valign="bottom" width="94"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">225<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">3,2<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"></td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1800<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 70.85pt;" valign="bottom" width="94"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">450<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1,7<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 7;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">6<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1090<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 70.85pt;" valign="bottom" width="94"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">182<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">3,9<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"></td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">2600<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 70.85pt;" valign="bottom" width="94"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">433<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1,7<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 8;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">8<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1390<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 70.85pt;" valign="bottom" width="94"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">174<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">4,1<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"></td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">3325<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 70.85pt;" valign="bottom" width="94"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">416<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1,8<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 9;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">10<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1630<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 70.85pt;" valign="bottom" width="94"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">163<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">4,4<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"></td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: red; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">4120<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 70.85pt;" valign="bottom" width="94"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: red; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">412<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: red; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1,8<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15.75pt; mso-yfti-irow: 10; mso-yfti-lastrow: yes;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) windowtext windowtext; border-style: none none solid solid; border-width: 0px 0px 1pt 1pt; height: 15.75pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">12<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none solid; border-width: 0px 0px 1pt; height: 15.75pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: red; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1890<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none solid; border-width: 0px 0px 1pt; height: 15.75pt; padding: 0cm 3.5pt; width: 70.85pt;" valign="bottom" width="94"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: red; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">158<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none solid; border-width: 0px 0px 1pt; height: 15.75pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: red; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">4,5<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none solid; border-width: 0px 0px 1pt; height: 15.75pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none solid; border-width: 0px 0px 1pt; height: 15.75pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">5000<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none solid; border-width: 0px 0px 1pt; height: 15.75pt; padding: 0cm 3.5pt; width: 70.85pt;" valign="bottom" width="94"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">417<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext windowtext rgb(0, 0, 0); border-style: none solid solid none; border-width: 0px 1pt 1pt 0px; height: 15.75pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1,8<o:p></o:p></span></div>
</td>
</tr>
</tbody></table>
<br />
<br />
<table border="0" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; height: 245px; margin: auto auto auto 2.75pt; mso-padding-alt: 0cm 3.5pt 0cm 3.5pt; mso-yfti-tbllook: 1184; width: 583px;">
<tbody>
<tr style="height: 15pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td nowrap="" style="background-color: transparent; border-color: windowtext rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: solid none none solid; border-width: 1pt 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
<td colspan="2" nowrap="" style="background-color: transparent; border-color: windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: solid none none; border-width: 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 120pt;" valign="bottom" width="160"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">Intel 4x E7-4870<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: solid none none; border-width: 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: windowtext windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: solid solid none none; border-width: 1pt 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 1;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
<td colspan="2" nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 120pt;" valign="bottom" width="160"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">10 cœurs/CPU<o:p></o:p></span></div>
</td>
<td colspan="2" nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) black rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 120pt;" valign="bottom" width="160"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">4 canaux mémoire<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 2;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 47.1pt;" valign="bottom" width="63"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">2,4 Ghz<o:p></o:p></span></div>
</td>
<td colspan="2" nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 132.9pt;" valign="bottom" width="177"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">2 threads / cœur<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 3;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">#threads<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 47.1pt;" valign="bottom" width="63"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">ms<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 72.9pt;" valign="bottom" width="97"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">perf/thread<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"></td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 4;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 47.1pt;" valign="bottom" width="63"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1744<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 72.9pt;" valign="bottom" width="97"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1744<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1,0<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 5;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">2<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 47.1pt;" valign="bottom" width="63"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1733<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 72.9pt;" valign="bottom" width="97"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">867<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">2,0<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 6;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">4<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 47.1pt;" valign="bottom" width="63"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">2089<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 72.9pt;" valign="bottom" width="97"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">522<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">3,3<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 7;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">40<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 47.1pt;" valign="bottom" width="63"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">2712<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 72.9pt;" valign="bottom" width="97"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">68<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">25,7<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 8;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">80<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 47.1pt;" valign="bottom" width="63"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: red; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">4484<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 72.9pt;" valign="bottom" width="97"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: red; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">56<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: red; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">31,1<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 9;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">120<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 47.1pt;" valign="bottom" width="63"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">8350<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 72.9pt;" valign="bottom" width="97"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">70<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">25,1<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 10;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">160<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 47.1pt;" valign="bottom" width="63"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">10433<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 72.9pt;" valign="bottom" width="97"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">65<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">26,7<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15.75pt; mso-yfti-irow: 11; mso-yfti-lastrow: yes;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) windowtext windowtext; border-style: none none solid solid; border-width: 0px 0px 1pt 1pt; height: 15.75pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">320<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none solid; border-width: 0px 0px 1pt; height: 15.75pt; padding: 0cm 3.5pt; width: 47.1pt;" valign="bottom" width="63"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">20566<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none solid; border-width: 0px 0px 1pt; height: 15.75pt; padding: 0cm 3.5pt; width: 72.9pt;" valign="bottom" width="97"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">64<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none solid; border-width: 0px 0px 1pt; height: 15.75pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">27,1<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext windowtext rgb(0, 0, 0); border-style: none solid solid none; border-width: 0px 1pt 1pt 0px; height: 15.75pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
</tr>
</tbody></table>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Arial","sans-serif";"><o:p> </o:p></span></div>
What do we learn? When using memory, one of the most important thing is the number of memory channels. We also learn that the latest Intel CPUs (3870 and 3930) are really good.<br />
Note that in these benchmarks there is no concurrent access in memory: the memory is splitted into several parts at the beginning.<br />
<br />
Can we observe these results for all problems? The answer is NO. When, we do not require so much memory the results are quite different, as shown by the following tables; for these benchmarks, the same protocol is used, but the problem which is solved by each thread requires at most 1Mo of memory.<br />
<br />
<br />
<table border="0" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; height: 222px; margin: auto auto auto 2.75pt; mso-padding-alt: 0cm 3.5pt 0cm 3.5pt; mso-yfti-tbllook: 1184; width: 591px;">
<tbody>
<tr style="height: 15pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td nowrap="" style="background-color: transparent; border-color: windowtext rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: solid none none solid; border-width: 1pt 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: solid none none; border-width: 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">Intel i7 920<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: solid none none; border-width: 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: solid none none; border-width: 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: solid none none; border-width: 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
<td colspan="2" nowrap="" style="background-color: transparent; border-color: windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: solid none none; border-width: 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 120pt;" valign="bottom" width="160"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">Intel i7 3820<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: windowtext windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: solid solid none none; border-width: 1pt 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 1;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">4 cœurs<o:p></o:p></span></div>
</td>
<td colspan="2" nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 120pt;" valign="bottom" width="160"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">2 canaux mémoire<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"></td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">4 cœurs<o:p></o:p></span></div>
</td>
<td colspan="2" nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) black rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 130.85pt;" valign="bottom" width="174"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">4 canaux mémoire<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 2;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">2,66 Ghz<o:p></o:p></span></div>
</td>
<td colspan="2" nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 120pt;" valign="bottom" width="160"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">2 threads / cœur<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"></td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">3,6 Ghz<o:p></o:p></span></div>
</td>
<td colspan="2" nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) black rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 130.85pt;" valign="bottom" width="174"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">2 threads / cœur<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 3;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">#threads<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">ms<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">perf/thread<o:p></o:p></span></div>
</td>
<td colspan="2" nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 120pt;" valign="bottom" width="160"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">ratio / 1 thread<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">ms<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 70.85pt;" valign="bottom" width="94"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">perf/thread<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 4;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1790<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1790<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1,0<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"></td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1100<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 70.85pt;" valign="bottom" width="94"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1100<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1,0<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 5;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">2<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1790<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">895<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">2,0<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"></td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1140<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 70.85pt;" valign="bottom" width="94"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">570<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1,9<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 6;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">4<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">2000<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">500<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">3,6<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"></td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1300<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 70.85pt;" valign="bottom" width="94"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">325<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">3,4<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 7;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">6<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">2800<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">467<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">3,8<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"></td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1830<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 70.85pt;" valign="bottom" width="94"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">305<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">3,6<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 8;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">8<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: red; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">3610<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: red; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">451<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: red; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">4,0<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"></td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">2260<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 70.85pt;" valign="bottom" width="94"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">283<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">3,9<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 9;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">10<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">4500<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">450<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">4,0<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"></td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">2810<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 70.85pt;" valign="bottom" width="94"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">281<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">3,9<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15.75pt; mso-yfti-irow: 10; mso-yfti-lastrow: yes;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) windowtext windowtext; border-style: none none solid solid; border-width: 0px 0px 1pt 1pt; height: 15.75pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">12<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none solid; border-width: 0px 0px 1pt; height: 15.75pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">5400<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none solid; border-width: 0px 0px 1pt; height: 15.75pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">450<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none solid; border-width: 0px 0px 1pt; height: 15.75pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">4,0<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none solid; border-width: 0px 0px 1pt; height: 15.75pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none solid; border-width: 0px 0px 1pt; height: 15.75pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: red; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">3300<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none solid; border-width: 0px 0px 1pt; height: 15.75pt; padding: 0cm 3.5pt; width: 70.85pt;" valign="bottom" width="94"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: red; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">275<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext windowtext rgb(0, 0, 0); border-style: none solid solid none; border-width: 0px 1pt 1pt 0px; height: 15.75pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: red; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">4,0<o:p></o:p></span></div>
</td>
</tr>
</tbody></table>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Arial","sans-serif";"><o:p> </o:p></span></div>
<br />
<table border="0" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; height: 224px; margin: auto auto auto 2.75pt; mso-padding-alt: 0cm 3.5pt 0cm 3.5pt; mso-yfti-tbllook: 1184; width: 590px;">
<tbody>
<tr style="height: 15pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td nowrap="" style="background-color: transparent; border-color: windowtext rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: solid none none solid; border-width: 1pt 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
<td colspan="2" nowrap="" style="background-color: transparent; border-color: windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: solid none none; border-width: 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 120pt;" valign="bottom" width="160"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">Intel i7 3930<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: solid none none; border-width: 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: solid none none; border-width: 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
<td colspan="2" nowrap="" style="background-color: transparent; border-color: windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: solid none none; border-width: 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 120pt;" valign="bottom" width="160"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">AMD FX8150<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: windowtext windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: solid solid none none; border-width: 1pt 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 1;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">6 cœurs<o:p></o:p></span></div>
</td>
<td colspan="2" nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 130.85pt;" valign="bottom" width="174"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">4 canaux mémoire<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"></td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">8 cœurs<o:p></o:p></span></div>
</td>
<td colspan="2" nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) black rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 130.85pt;" valign="bottom" width="174"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">2 canaux mémoire<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 2;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">3,2 Ghz<o:p></o:p></span></div>
</td>
<td colspan="2" nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 130.85pt;" valign="bottom" width="174"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">2 threads / cœur<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"></td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">3,6 Ghz<o:p></o:p></span></div>
</td>
<td colspan="2" nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) black rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 130.85pt;" valign="bottom" width="174"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1 thread/cœur<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 3;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">#threads<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">ms<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 70.85pt;" valign="bottom" width="94"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">perf/thread<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"></td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"></td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">ms<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 70.85pt;" valign="bottom" width="94"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">perf/thread<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 4;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1210<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 70.85pt;" valign="bottom" width="94"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1210<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1,0<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"></td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">2000<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 70.85pt;" valign="bottom" width="94"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">2000<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1,0<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 5;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">2<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1210<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 70.85pt;" valign="bottom" width="94"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">605<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">2,0<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"></td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">2051<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 70.85pt;" valign="bottom" width="94"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1026<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">2,0<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 6;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">4<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1285<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 70.85pt;" valign="bottom" width="94"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">321<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">3,8<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"></td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">2160<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 70.85pt;" valign="bottom" width="94"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">540<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">3,7<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 7;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">6<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1650<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 70.85pt;" valign="bottom" width="94"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">275<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">4,4<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"></td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">2625<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 70.85pt;" valign="bottom" width="94"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">438<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">4,6<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 8;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">8<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1880<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 70.85pt;" valign="bottom" width="94"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">235<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">5,1<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"></td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: red; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">2830<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 70.85pt;" valign="bottom" width="94"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: red; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">354<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: red; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">5,7<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 9;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">10<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">2240<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 70.85pt;" valign="bottom" width="94"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">224<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">5,4<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"></td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">3850<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 70.85pt;" valign="bottom" width="94"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">385<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">5,2<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15.75pt; mso-yfti-irow: 10; mso-yfti-lastrow: yes;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) windowtext windowtext; border-style: none none solid solid; border-width: 0px 0px 1pt 1pt; height: 15.75pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">12<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none solid; border-width: 0px 0px 1pt; height: 15.75pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: red; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">2620<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none solid; border-width: 0px 0px 1pt; height: 15.75pt; padding: 0cm 3.5pt; width: 70.85pt;" valign="bottom" width="94"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: red; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">218<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none solid; border-width: 0px 0px 1pt; height: 15.75pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: red; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">5,5<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none solid; border-width: 0px 0px 1pt; height: 15.75pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none solid; border-width: 0px 0px 1pt; height: 15.75pt; padding: 0cm 3.5pt; width: 49.15pt;" valign="bottom" width="66"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">4490<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none solid; border-width: 0px 0px 1pt; height: 15.75pt; padding: 0cm 3.5pt; width: 70.85pt;" valign="bottom" width="94"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">374<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext windowtext rgb(0, 0, 0); border-style: none solid solid none; border-width: 0px 1pt 1pt 0px; height: 15.75pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">5,3<o:p></o:p></span></div>
</td>
</tr>
</tbody></table>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Arial","sans-serif";"><o:p> </o:p></span></div>
<br />
<table border="0" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; margin: auto auto auto 2.75pt; mso-padding-alt: 0cm 3.5pt 0cm 3.5pt; mso-yfti-tbllook: 1184; width: 400px;">
<tbody>
<tr style="height: 15pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td nowrap="" style="background-color: transparent; border-color: windowtext rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: solid none none solid; border-width: 1pt 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
<td colspan="2" nowrap="" style="background-color: transparent; border-color: windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: solid none none; border-width: 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 120pt;" valign="bottom" width="160"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">Intel 4x E7-4870<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: solid none none; border-width: 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: windowtext windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: solid solid none none; border-width: 1pt 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 1;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
<td colspan="2" nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 120pt;" valign="bottom" width="160"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">10 cœurs/CPU<o:p></o:p></span></div>
</td>
<td colspan="2" nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) black rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 120pt;" valign="bottom" width="160"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">4 canaux mémoire<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 2;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 47.1pt;" valign="bottom" width="63"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">2,4 Ghz<o:p></o:p></span></div>
</td>
<td colspan="2" nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 132.9pt;" valign="bottom" width="177"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">2 threads / cœur<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 3;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">#threads<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 47.1pt;" valign="bottom" width="63"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">ms<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 72.9pt;" valign="bottom" width="97"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">perf/thread<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"></td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 4;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 47.1pt;" valign="bottom" width="63"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1910<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 72.9pt;" valign="bottom" width="97"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1910<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1,0<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 5;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">2<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 47.1pt;" valign="bottom" width="63"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1920<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 72.9pt;" valign="bottom" width="97"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">960<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">2,0<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 6;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">4<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 47.1pt;" valign="bottom" width="63"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">1920<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 72.9pt;" valign="bottom" width="97"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">480<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">4,0<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 7;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">40<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 47.1pt;" valign="bottom" width="63"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">3030<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 72.9pt;" valign="bottom" width="97"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">76<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">25,2<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 8;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">80<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 47.1pt;" valign="bottom" width="63"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: red; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">4080<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 72.9pt;" valign="bottom" width="97"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: red; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">51<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: red; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">37,5<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 9;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">120<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 47.1pt;" valign="bottom" width="63"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">6230<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 72.9pt;" valign="bottom" width="97"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">52<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">36,8<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15pt; mso-yfti-irow: 10;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none none solid; border-width: 0px 0px 0px 1pt; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">160<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 47.1pt;" valign="bottom" width="63"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">8230<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 72.9pt;" valign="bottom" width="97"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">51<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border: rgb(0, 0, 0); height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">37,1<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext rgb(0, 0, 0) rgb(0, 0, 0); border-style: none solid none none; border-width: 0px 1pt 0px 0px; height: 15pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15.75pt; mso-yfti-irow: 11; mso-yfti-lastrow: yes;">
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) windowtext windowtext; border-style: none none solid solid; border-width: 0px 0px 1pt 1pt; height: 15.75pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">320<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none solid; border-width: 0px 0px 1pt; height: 15.75pt; padding: 0cm 3.5pt; width: 47.1pt;" valign="bottom" width="63"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">16260<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none solid; border-width: 0px 0px 1pt; height: 15.75pt; padding: 0cm 3.5pt; width: 72.9pt;" valign="bottom" width="97"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">51<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) rgb(0, 0, 0) windowtext; border-style: none none solid; border-width: 0px 0px 1pt; height: 15.75pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: right;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";">37,6<o:p></o:p></span></div>
</td>
<td nowrap="" style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext windowtext rgb(0, 0, 0); border-style: none solid solid none; border-width: 0px 1pt 1pt 0px; height: 15.75pt; padding: 0cm 3.5pt; width: 60pt;" valign="bottom" width="80"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Calibri","sans-serif"; font-size: 11pt; mso-fareast-font-family: "Times New Roman";"> <o:p></o:p></span></div>
</td>
</tr>
</tbody></table>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="color: black; font-family: "Arial","sans-serif";"><o:p> </o:p></span></div>
In this case, it is clear that the results of the AMD CPU are better than in the previous case. However, it is still clearly outperformed by recent Intel CPUs.<br />
<br />
For those who can be interested, here are the results for an Intel i7 2600<br />
<br />
<table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse; width: 240px;">
<colgroup><col span="3" style="width: 60pt;" width="80"></col>
<tbody>
<tr height="20" style="height: 15pt;">
<td height="20" style="background-color: transparent; border: 0px black; height: 15pt; width: 60pt;" width="80"><span style="font-family: Calibri;">i7 2600</span></td>
<td style="background-color: transparent; border: 0px black; width: 60pt;" width="80"></td>
<td style="background-color: transparent; border: 0px black; width: 60pt;" width="80"></td>
</tr>
<tr height="20" style="height: 15pt;">
<td height="20" style="background-color: transparent; border: 0px black; height: 15pt;"><span style="font-family: Calibri;">ms</span></td>
<td style="background-color: transparent; border: 0px black;"><span style="font-family: Calibri;">perf/thread</span></td>
<td style="background-color: transparent; border: 0px black;"></td>
</tr>
<tr height="20" style="height: 15pt;">
<td align="right" class="xl65" height="20" style="background-color: transparent; border: 0px black; height: 15pt;"><span style="font-family: Calibri;">685</span></td>
<td align="right" class="xl65" style="background-color: transparent; border: 0px black;"><span style="font-family: Calibri;">685</span></td>
<td align="right" class="xl67" style="background-color: transparent; border: 0px black;"><span style="font-family: Calibri;">1,0</span></td>
</tr>
<tr height="20" style="height: 15pt;">
<td align="right" class="xl65" height="20" style="background-color: transparent; border: 0px black; height: 15pt;"><span style="font-family: Calibri;">841</span></td>
<td align="right" class="xl65" style="background-color: transparent; border: 0px black;"><span style="font-family: Calibri;">421</span></td>
<td align="right" class="xl67" style="background-color: transparent; border: 0px black;"><span style="font-family: Calibri;">1,6</span></td>
</tr>
<tr height="20" style="height: 15pt;">
<td align="right" class="xl65" height="20" style="background-color: transparent; border: 0px black; height: 15pt;"><span style="font-family: Calibri;">1423</span></td>
<td align="right" class="xl65" style="background-color: transparent; border: 0px black;"><span style="font-family: Calibri;">356</span></td>
<td align="right" class="xl67" style="background-color: transparent; border: 0px black;"><span style="font-family: Calibri;">1,9</span></td>
</tr>
<tr height="20" style="height: 15pt;">
<td align="right" class="xl66" height="20" style="background-color: transparent; border: 0px red; height: 15pt;"><span style="color: red; font-family: Calibri;">1943</span></td>
<td align="right" class="xl66" style="background-color: transparent; border: 0px red;"><span style="color: red; font-family: Calibri;">324</span></td>
<td align="right" class="xl68" style="background-color: transparent; border: 0px red;"><span style="color: red; font-family: Calibri;">2,1</span></td>
</tr>
<tr height="20" style="height: 15pt;">
<td align="right" class="xl70" height="20" style="background-color: transparent; border: 0px windowtext; height: 15pt;"><span style="font-family: Calibri;">2693</span></td>
<td align="right" class="xl70" style="background-color: transparent; border: 0px windowtext;"><span style="font-family: Calibri;">337</span></td>
<td align="right" class="xl69" style="background-color: transparent; border: 0px windowtext;"><span style="font-family: Calibri;">2,0</span></td>
</tr>
<tr height="20" style="height: 15pt;">
<td align="right" class="xl65" height="20" style="background-color: transparent; border: 0px black; height: 15pt;"><span style="font-family: Calibri;">3532</span></td>
<td align="right" class="xl65" style="background-color: transparent; border: 0px black;"><span style="font-family: Calibri;">353</span></td>
<td align="right" class="xl67" style="background-color: transparent; border: 0px black;"><span style="font-family: Calibri;">1,9</span></td>
</tr>
<tr height="20" style="height: 15pt;">
<td align="right" class="xl65" height="20" style="background-color: transparent; border: 0px black; height: 15pt;"><span style="font-family: Calibri;">4338</span></td>
<td align="right" class="xl70" style="background-color: transparent; border: 0px windowtext;"><span style="font-family: Calibri;">362</span></td>
<td align="right" class="xl67" style="background-color: transparent; border: 0px black;"><span style="font-family: Calibri;">1,9</span></td>
</tr>
</tbody></colgroup></table>
<br />
I also compare Windows (VS 2012) and Linux (GCC latest version) on the very same machine (core I7 3930): the maximum difference is 10% (Windows is faster when we do not require too much memory)<br />
<br />
These results give me some inputs on my quest of 100x improvement machine.<br />
<br />
These results also show that we have to be careful when giving results for parallelisms. The impact of the machine that is used is more important than for sequential resultJean-Charles Réginhttp://www.blogger.com/profile/06540516780781311246noreply@blogger.com0tag:blogger.com,1999:blog-3001120404365621770.post-71456391005984521142012-08-20T00:41:00.000-07:002012-08-20T00:41:43.852-07:00When an OR book mention CP<br />
I just found a book “Model Building in Mathematical Programming” by H. Paul Williams on the desktop of a colleague. I opened it out of curiosity… One page (page 16 is dedicated to CP). Probably the author wanted to be exhaustive and mention CP but honestly I would prefer he forgot to speak about it ;-)<br />
<br />
<i>“The methods used (in CP) are mathematically less sophisticated”</i><br />
<br />
This kind of sentence should be avoided when you speak about a domain that you probably don’t know much especially when two sentences later you explain forward checking for alldiff and forget to mention the matching+scc algorithm of J-C Régin used in every CP Solvers. The author clearly ignores all the mathematical algorithms that are used inside global constraints (just to name a few: Network Flow Constraint, Bounded Knapsack, (soft)-GCC, …). Ok, all the global constraints did not exist at the time of publication of the book but GCC, cost-gcc, already existed.<br />
<br />
<i>“CP is mainly useful where a problem has no objective function. It lacks the ability to prove optimality (apart from by complete enumeration).”</i><br />
<br />
Not true of course. B&B has been adapted for CP long time ago. When the variable you want to minimize in the scope of a global constraint you can get very good lower bounds to prune you B&B search tree (see my previous post: <a href="http://cp-is-fun.blogspot.be/2011/04/yes-we-can-optimize.html">yes we can optimize</a>). The author probably ignores that CP is the state of the art exact method to optimize scheduling problems for instance. By the way, I personally find that filtering algorithm for scheduling (edge finding, not-first not-last …) are quite sophisticated ;-)<br />
<br />
I have the feeling that this kind of very short review of CP in a well-known OR book can be really disastrous for CP. The reader who reads this and doesn’t know CP yet will surely not try to learn more about it. It this would be very sad because it’s really a fun, interesting and sophisticated approach to solve combinatorial optimization problems. Any way, this book is surely excellent to learn how to build mathematical programming, which it’s main objective.<br />
<div>
<br /></div>
pschaushttp://www.blogger.com/profile/10578391475922351456noreply@blogger.com4tag:blogger.com,1999:blog-3001120404365621770.post-74263241595476407262012-04-26T07:19:00.000-07:002012-04-26T07:19:48.311-07:00Laurent Perron's talk last year at CPI just read the slides of the <a href="http://www.dmi.unipg.it/cp2011/invited.html#">invited talk of Laurent Perron</a> last year at <a href="http://www.dmi.unipg.it/cp2011/index.html">CP conference</a>. I found them very instructive.
Here are 3 slides that particularly caught my attention:
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEji3xMnLhqVjvDSB4UXJwPLG99zie37o1EMp4_EovLptONeVw4s4309o9YVmLELAkRKQLgqdXIfAnJLHqdlgrqmzp9-6ivpvT8GOitu-PILUcNa8pJqC3eAwJdAfEXlYDxwweLE4c4ija0/s1600/Screen+Shot+2012-04-26+at+15.11.51.png" imageanchor="1" style="margin-left:1em; margin-right:1em"><img border="0" height="298" width="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEji3xMnLhqVjvDSB4UXJwPLG99zie37o1EMp4_EovLptONeVw4s4309o9YVmLELAkRKQLgqdXIfAnJLHqdlgrqmzp9-6ivpvT8GOitu-PILUcNa8pJqC3eAwJdAfEXlYDxwweLE4c4ija0/s400/Screen+Shot+2012-04-26+at+15.11.51.png" /></a></div>
It’s great to see that CP is so much used at google. Even more than MIP! I guess it’s because CP is one of the most flexible technique you can find in combinatorial optimization. When it is mixed with LNS (CP + LS) it scales very well.
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgjNnddmKqLq20ljIE5698URBpYu73UopQaH4I2BS7xG7IYswetbisDI38-xBZ6d79rHhZBpbvQvStgZveE9_2MfpBejYLDpPOPstmjnYlYvyU-igY9XmEClCmA8reoC1i2nbRRUx0cEyA/s1600/Screen+Shot+2012-04-26+at+15.14.17.png" imageanchor="1" style="margin-left:1em; margin-right:1em"><img border="0" height="298" width="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgjNnddmKqLq20ljIE5698URBpYu73UopQaH4I2BS7xG7IYswetbisDI38-xBZ6d79rHhZBpbvQvStgZveE9_2MfpBejYLDpPOPstmjnYlYvyU-igY9XmEClCmA8reoC1i2nbRRUx0cEyA/s400/Screen+Shot+2012-04-26+at+15.14.17.png" /></a></div>
I can’t agree more with that one. I would also add an item to build the right graphical user interface for your application is also important and very time consuming. Unless you are in a very big team with specialists, this is also something you have to do.
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This slides is a bit arsh but probably so true. I guess the community should take it as a challenge and try to publish things that may be eventually used at google.
I find it very sad that it seems so difficult to publish implementation details.
It would be so nice to have for instance a paper of Laurent describing the architecture and design choices he made for or-tool solver. I hope the reviewers of CP this year (probably busy reading the papers now) will take this remark of Laurent into account ;-))pschaushttp://www.blogger.com/profile/10578391475922351456noreply@blogger.com0tag:blogger.com,1999:blog-3001120404365621770.post-21635221880955527042012-02-27T00:59:00.004-08:002012-02-27T01:07:19.078-08:00Asteroid is out! new open-source CBLS Solver ...<div style="text-align: center;"><span><u><br /></u></span></div><br /><div style="font-family: Georgia, serif; font-size: 100%; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal; ">Plenty of good news in the local search community these days!</div><div style="font-family: Georgia, serif; font-size: 100%; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal; ">But this one is even better since it is an open-source solver with a commercial friendly license (LGPL) and developed in Scala (my current favorite programming language).</div><div style="font-family: Georgia, serif; font-size: 100%; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal; ">This is a new CBLS solver developed by Renaud De Landtsheer at the <a href="http://www.cetic.be/">Cetic</a>.</div><div style="font-family: Georgia, serif; font-size: 100%; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal; ">This solver is very close to the constrained base local search and the models you would see in the <a href="http://mitpress.mit.edu/catalog/item/default.asp?ttype=2&tid=10664">Book</a> of Pascal Van Hentenryck and Laurent Michel.</div><div style="font-family: Georgia, serif; font-size: 100%; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal; ">I guess the name of this solver (<a href="https://forge.pallavi.be/projects/asteroid/wiki">Asteroid</a>) is an allusion to the pioneering CBLS system Comet:</div><div style="font-family: Georgia, serif; font-size: 100%; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal; "><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidyZjdrjdr4GKXqQrhJHIGkp4o7XnwX1qlW0xXib6HSgVjGYKiYr3HmnSUrGQfCNEAeHgJJmBQ_Kdi6Szr4I4gXGfTBzZ5PpnYLEuJm5LN6xWAQXgz1hUmjlc17nC_E-dq7Iqp7w223Hc/s1600/Asteroid-logo-small.png"><img src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidyZjdrjdr4GKXqQrhJHIGkp4o7XnwX1qlW0xXib6HSgVjGYKiYr3HmnSUrGQfCNEAeHgJJmBQ_Kdi6Szr4I4gXGfTBzZ5PpnYLEuJm5LN6xWAQXgz1hUmjlc17nC_E-dq7Iqp7w223Hc/s320/Asteroid-logo-small.png" border="0" alt="" id="BLOGGER_PHOTO_ID_5713738484435559042" style="display: block; margin-top: 0px; margin-right: auto; margin-bottom: 10px; margin-left: auto; text-align: center; cursor: pointer; width: 320px; height: 71px; " /></a></div><div style="font-family: Georgia, serif; font-size: 100%; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal; ">Cetic is a research center in Computer Science in Belgium. I’m very happy they start to invest into optimization and also to open-source it.</div><div style="font-family: Georgia, serif; font-size: 100%; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal; ">Here is an n-queens model to give you a taste of it:</div><br /><br /><pre name="code" class="scala"><br /> val N:Int=40<br /> val min = 0<br /> val max = N-1<br /> val range:Range = Range(0,N)<br /> val tabulength = 1<br /> val m: Model = new Model(false)<br /> val MaxIT = 10000<br /><br /> println("NQueens(" + N + ")")<br /> val Queens:Array[IntVar] = new Array[IntVar](N)<br /> for (q <- range){Queens(q) = new IntVar(m, min, max, q, "queen" + q)}<br /><br /> val c:ConstraintSystem = new ConstraintSystem(m)<br /><br /> //c.Post(AllDiff(Queens)) handled trough permutations<br /> c.Post(AllDiff(for ( q <- range) yield (q plus Queens(q)).ToIntVar))<br /> c.Post(AllDiff(for ( q <- range) yield (q minus Queens(q)).ToIntVar))<br /><br /> c.close<br /> m.close<br /><br /> var it:Int =0<br /><br /> val Tabu = (for(q <- range)yield -1).toArray<br /><br /> var longueurplateau = 0;<br /> while((c.Violation.GetValue() > 0) && (it < MaxIT)){<br /> val oldviolation:Int = c.Violation<br /> val allowedqueens = range.filter(q => Tabu(q) < it)<br /> val (q1,q2):(Int,Int) = SelectMin2(allowedqueens,allowedqueens, (q1:Int, q2:Int) => c.GetSwapViol(Queens(q1),Queens(q2)), (q1:Int,q2:Int) => q1 != q2)<br /><br /> Queens(q1) :=: Queens(q2)<br /> Tabu(q1) = it + tabulength<br /> Tabu(q2) = it + tabulength<br /><br /> it += 1<br /> println("it: " + it + " " + c.Violation + " (swapped "+ q1 + " and " + q2 + ")")<br /> if(oldviolation <= c.Violation.GetValue()) longueurplateau+=1 else longueurplateau = 0<br /><br /> if (longueurplateau > 5){<br /> println("jump away")<br /> for (i <- 1 to N/5){<br /> Queens(SelectFrom(range)) :=: Queens(SelectFrom(range))<br /> }<br /> longueurplateau = 0<br /> }<br /> }<br /> println(c.Violation)<br /> println(m.GetSolution(true))<br /> }<br /></pre>pschaushttp://www.blogger.com/profile/10578391475922351456noreply@blogger.com8tag:blogger.com,1999:blog-3001120404365621770.post-43978142270714826062012-02-24T00:30:00.005-08:002012-02-24T00:40:50.738-08:00You need to understand a bit the technology you use to build good models!<span ><span style="font-size: 100%;">I just read yesterday evening the paper published in 4OR about LocalSolver to understand a bit more the technology behind. I would like to add a few comments on the results section in particular the results on Steel Mill Slab problem that I know quite well (a kind of cutting stock problem with several cutting lengths and a color constraint on the patterns). </span></span><br /><br /><span ><span style="font-size: 100%;">Just a reminder on the progresses to solve this problem over the last years:</span></span><br /><br /><span ><span style="font-size: 100%;">Antoine Gargani and Philippe Refalo closed the CSPLib instance with CP+LNS in 2006. Then Pascal Van Hentenryck and Laurent Michel explained that LNS is not necessary if you break dynamically the symmetries. A bit later, on more difficult instances the best results where obtained with CBLS using an exact differential invariant that you can implement in 5 lines of Comet. Finally Stefan Heinz had the last word closing the most difficult instances with MIP (SCIP) by generating all the columns in advance (not so many).</span></span><br /><br /><span ><span style="font-size: 100%;">So you can imagine how surprised I was reading in this section that LocalSolver outperforms MIP (Cplex) and CBLS ?!?!? </span></span><br /><span ><span style="font-size: 100%;">But now I think I understand how the results where conducted (please correct me if I’m wrong). My understanding is that they used the same kind of models (0/1 decision variables) for LocalSolver, CBLS and Cplex. In that case the results make complete sense because:</span></span><br /><span ><span style="font-size: 100%;">- in MIP you’ll get all the symmetries as would get with a completely naïve bin-backing formulation (nobody having a minimum background in OR would never model a bin-packing problem in MIP like that).</span></span><br /><span ><span style="font-size: 100%;">- in CBLS the differentiation of the objective will always give you 0 which means you are making completely random moves.</span></span><br /><br /><span ><span style="font-size: 100%;">Unfortunately this is not really explained (the models are not given, and the CBLS moves neither) and I don’t want that someone reading this article think that CBLS is not great to solve complex problems (with a correct differentiation, CBLS solves the steel mill slab instance of CSPLib with about twenty greedy swaps ;-) )</span></span><br /><span ><span style="font-size: 100%;">If you use CBLS you should understand when the differentiation of the objective is correct, what a differential invariant is, and you should certainly not build naïve CBLS models in the same way, as you never model with 0/1 variables in CP. </span></span><br /><br /><span ><span style="font-size: 100%;"><b>In conclusion, Optimization is quite complex, you need to have a minimum of understanding on how to build good models for the underlying technology you are using. I personally don’t believe that good modelers (in MIP, LS or CP) will be replaced very soon by automatic tools to get the best possible results.</b></span></span><br /><br /><span ><span style="font-size: 100%;">Two great blogs where you can read nice things on the art of good modeling and good formulation are:</span></span><br /><ul><li style="font-family: Georgia, serif; font-size: 100%; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal; "><span style="font-size: 100%; "><a href="http://yetanothermathprogrammingconsultant.blogspot.com/">http://yetanothermathprogrammingconsultant.blogspot.com/</a></span></li><li><span ><a href="http://orinanobworld.blogspot.com">http://orinanobworld.blogspot.com</a>/</span></li></ul><div><span ><br /></span></div>pschaushttp://www.blogger.com/profile/10578391475922351456noreply@blogger.com13tag:blogger.com,1999:blog-3001120404365621770.post-46081440624851570862012-02-22T11:41:00.000-08:002012-02-22T13:19:03.716-08:00Local Solver is out<a href="http://www.localsolver.com">LocalSolver</a> is a back-box commercial local search solver developed at Bouygues.<br />
It's free for academics but since I'm not academic I cannot fully try it. Here are some thoughts after reading a bit their website:<br />
It seems very nice and the results are quite impressive but to me it doesn't mean that tree search methods are dead.<br />
Approaches like LNS (large neighborhood search) are very powerful to explore complex neighborhood with tree search methods like CP.<br />
Also counting the number of 0-1 variables and the number of moves per second is not the argument that I prefer to judge the quality of the solution I can potentially get with a solver. <br />
I prefer much more to have some kind of control to do very complex moves and self designed search as CBLS in Comet.<br />
The thesis of Sebastien Mouthuy "<a href="http://www.info.ucl.ac.be/~yde/Papers/thesis-smouthuy2011.pdf">Constraint-based very Large-Scale Neighborhood Search</a>" is very nice on this topic of building very complex moves.<br />
Anyway, it's always a good news to see new technology in optimization coming out. I'm looking forward to read feedback or user experience from the local search community. Maybe this will become the future "cplex" for local search i.e. a kind of standard benchmarking tool...pschaushttp://www.blogger.com/profile/10578391475922351456noreply@blogger.com0tag:blogger.com,1999:blog-3001120404365621770.post-15171983910324260472012-02-18T00:45:00.006-08:002012-02-18T00:59:10.191-08:00Hexiom Puzzle<div style="text-align: left;"><span style="font-family: Georgia, serif; font-size: 100%; text-align: left; ">Hexiom is a very interesting game that you can play online </span><a href="http://www.kongregate.com/games/Moonkey/hexiom" style="font-family: Georgia, serif; font-size: 100%; text-align: left; ">here</a></div><div style="font-family: Georgia, serif; font-size: 100%; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal; "><div><span><br /></span></div><div><span><i>“The object of Hexiom is to arrange all tiles in a way that they are adjacent to exactly the number of other tiles as they are showing.”</i></span></div><div><span><br /></span></div><div><span>Two solutions are for instance:</span></div></div><div style="font-family: Georgia, serif; font-size: 100%; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal; "><br /></div><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhLfFA3vhlWMsjgjklYeUAZn5hyphenhyphen1auTVJYXa4sMD8knwu068ziLuxcW45yqbpTBWmj7sYAR7PJPkJuVZDuQSlzQls8cq_6o6ezDfefnfZggAGFxHflqMRgSoB2-bf1EPhFk3ePkGrTrcho/s1600/hexiom2.jpg" style="font-family: Georgia, serif; font-size: 100%; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal; "><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 296px; height: 295px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhLfFA3vhlWMsjgjklYeUAZn5hyphenhyphen1auTVJYXa4sMD8knwu068ziLuxcW45yqbpTBWmj7sYAR7PJPkJuVZDuQSlzQls8cq_6o6ezDfefnfZggAGFxHflqMRgSoB2-bf1EPhFk3ePkGrTrcho/s320/hexiom2.jpg" border="0" alt="" id="BLOGGER_PHOTO_ID_5710395287883448754" /></a><div style="font-family: Georgia, serif; font-size: 100%; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal; "><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgwY8LZEFRKNyS0g1nCZMqesRjj66uZ56613laiyLxrAkMBv90iTuF_5MJNMJj0CRRAgwTGzbakj2T_kLzfeidodpOvvcjfmbJIVYjv9pPy2noRrUjsWnWyA9o3ezj-fbzdG4OPjA76t7w/s1600/hexiom.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 296px; height: 297px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgwY8LZEFRKNyS0g1nCZMqesRjj66uZ56613laiyLxrAkMBv90iTuF_5MJNMJj0CRRAgwTGzbakj2T_kLzfeidodpOvvcjfmbJIVYjv9pPy2noRrUjsWnWyA9o3ezj-fbzdG4OPjA76t7w/s320/hexiom.jpg" border="0" alt="" id="BLOGGER_PHOTO_ID_5710395159065631938" /></a><div><br /></div><div><span>This puzzle can be solved with CP in a nice way (like most of the problems of course ;-)). </span></div><div><span>If you don’t want to see my model right now, just think about which decision variables and constraints you would use before continuing the reading of this post.</span></div><div><span><br /></span></div><div><span>I use 3 types of variables in this model:</span></div><div><span><br /></span></div><div><span>1)<span class="Apple-tab-span" style="white-space:pre"> </span>Type1: I call them used(i) with domain {0,1} to tell whether or not there is a tile in position i.</span></div><div><span>2)<span class="Apple-tab-span" style="white-space:pre"> </span>Type2: I call them nbNeighbors(i) is a variable representing the number of neighboring tiles of position i. The domain of these should be {0,1,2,3,4,5,6} because tiles are hexagons</span></div><div><span>3)<span class="Apple-tab-span" style="white-space:pre"> </span>Type3: I call them card(i). Those are almost the same as Type 2 but I also include 7 so their domain will be be {0,1,2,3,4,5,6,7}. It will become clear with the explanation on the constraints why we also need Type3 variables.</span></div><div><span><br /></span></div><div><span>Now the constraints:</span></div><div><span><br /></span></div><div><span>If you have for instance in input 3,4,0,2,2… it means that you must have one tile with 3 adjacent tiles, one tile with 4 adjacent ones, one isolated tile, two tiles with two adjacent tiles, ….</span></div><div><span><br /></span></div><div><span>All of this can be imposed with just one Global Cardinality Constraint (<a href="http://www.emn.fr/z-info/sdemasse/gccat/Cglobal_cardinality.html">GCC </a>) posted on the card variables. The problem is that we don’t want to count a value in the card variables if there is not tile placed in this position. This is why I introduced the value 7 in the domain of the card variables: If there is not tile in a position i, card(i) will take value 7 rather than taking as value the number of adjacent tiles to position I (i.e. nbNeighbors(i)). Of course in our GCC the number of occurrences for value 7 is not constrained.</span></div><div><span><br /></span></div><div><span>To enforce the value 7 when there is no tile we have several options but not all of them are equivalent in terms of filtering. The optimal filtering is obtained by using a table constraint where you specify that the three variables (nbNeighbors(i),used(i),card(i)) altogether must be equal to one of those tuples: (0,0,7), (1,0,7), (2,0,7), (3,0,7), (4,0,7), (5,0,7), (6,0,7), (0,1,0), (1,1,1), (2,1,2), (3,1,3), (4,1,4), (5,1,5), (6,1,6)</span></div><div><span>Where nbNeighbors(i) is equal to sum(neighbors(i))(i => used(i)).</span></div><div><span>If you have a MIP background, you might be tempted to write something like:</span></div><div><span>card(i) == (used(i) * nbNeighbors + (1- used(i)) * 7)</span></div><div><span><br /></span></div><div><span>Unfortunately, using sum and prods to do it would have a weaker pruning than with the table option because products and summations mainly reason on the bounds of the domains in CP.</span></div><div><span><br /></span></div><div><span>In this model, it is also important to try to place tiles on the left branch and remove it on the right branch during the search tree exploration (optimistic heuristic). With this strategy we can find a solution to the hardest instance with only two backtracks!</span></div><div><span><br /></span></div><div><span>Here is it's solution (level 40)</span></div><div><span> <p class="p1"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiTBc25TdbI0Q0_gA11G04tQm4j7VwW-bUE8GiXRd4hdlgr7aXhRkD1KoJnpla6GJMIBgPKYZlniMWRcsYWLe_ECCzTGdriDTVOQxNO8kNEOvOUDINeOj8XLehAhjSoCkTkUlRqgl5xA9g/s1600/Screen+Shot+2012-02-18+at+09.56.38.png"><img src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiTBc25TdbI0Q0_gA11G04tQm4j7VwW-bUE8GiXRd4hdlgr7aXhRkD1KoJnpla6GJMIBgPKYZlniMWRcsYWLe_ECCzTGdriDTVOQxNO8kNEOvOUDINeOj8XLehAhjSoCkTkUlRqgl5xA9g/s320/Screen+Shot+2012-02-18+at+09.56.38.png" border="0" alt="" id="BLOGGER_PHOTO_ID_5710397164297358994" style="display: block; margin-top: 0px; margin-right: auto; margin-bottom: 10px; margin-left: auto; text-align: center; cursor: pointer; width: 320px; height: 319px; " /></a></p></span></div><div><span><br /></span></div><div><span>The source file of this model in Scampi is available <a href="https://bitbucket.org/pschaus/scampi/src/51fc9203fb6f/src/main/scala/scampi/cp/examples/Hexiom.scala">here</a> </span></div><div><span><br /></span></div><div><span>In the real hexiom, I think some positions of some tiles are forced. Of course it is not difficult to enfore that in this model (just force the value of card(i)).</span></div><div><span>An interesting variant to me would be to consider the overconstrained problem and try to place as many tiles as possible, or try to collect has many points as possible (number on the tiles).</span></div><div><span><br /></span></div><div><span>Let me know if you also implement a model for Hexiom in another system such that I attach a link to them on this blog.</span></div></div>pschaushttp://www.blogger.com/profile/10578391475922351456noreply@blogger.com2tag:blogger.com,1999:blog-3001120404365621770.post-37619219423514011402012-01-25T11:14:00.000-08:002012-01-25T11:20:38.611-08:00Introduction of the Orbel Wolsey-AwardYou are looking for a motivation to open-source one of your implementation related to Operations Research. The ORBEL <a href="http://www.n-side.com/wolsey-award">Wolsey-Award</a> may interest you!pschaushttp://www.blogger.com/profile/10578391475922351456noreply@blogger.com0tag:blogger.com,1999:blog-3001120404365621770.post-33897099856580960592012-01-15T02:58:00.001-08:002012-01-15T03:15:37.721-08:00Scampi Solver<img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 128px; height: 128px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiWQSPfoxWo71AErD40UIsonhu8kYNrfhtQMutlxTZotdVr8czQCwkOp2m6A5IE0gS-Gc-Zvosx9bTh3_fx0jKnBIrDJ1xkkwvHPkvDX_aX2Lw8F-tnzerabeE9McVZrD83H8qostRBQn4/s320/icon128.png" border="0" alt="" id="BLOGGER_PHOTO_ID_5697815539861999762" /><br />We just released our modest open-source scala library called <a href="http://bitbucket.org/pschaus/scampi">Scampi</a> to solve OR problems (currently CP, MIP, Derivative Free Optimization, Discrete Event Simulation): <div><div>Maybe you'll find it useful, maybe not but for us it was a way to promote Scala (a very nice language) and Operations Research.</div><div>Thank you to all the people from <a href="http://www.n-side.com/">n-Side</a> who have contributed or gave us some time to develop on Scampi and our two interns of this summer Cyrille Dejemeppe (UCL) who worked on the derivative free optimization package and Hrayr Kostanyan (ULB) who contributed on the linear programming package. We hope more documentation will come soon and please already accept our apologies for the bugs you may encounter if you try to use it.</div><div><br /></div><div><div><br /></div></div></div>pschaushttp://www.blogger.com/profile/10578391475922351456noreply@blogger.com2tag:blogger.com,1999:blog-3001120404365621770.post-61985602054941437742011-10-23T04:24:00.000-07:002011-10-23T04:28:30.385-07:00PhD Fellowship Award by IBM on CP topics<div><span class="Apple-style-span" ><span class="Apple-style-span" style="background-color: rgb(255, 255, 255); ">Patrick Albert (IBM) just announced the </span></span><span class="Apple-style-span" style="font-family: arial, sans-serif; font-size: 13px; background-color: rgb(255, 255, 255); "><span >PhD Fellowship Award by IBM for topics related to </span></span><span class="Apple-style-span" style="font-family: sans-serif; background-color: rgb(255, 255, 255); font-size: small; ">R&D </span><span class="Apple-style-span" style="font-family: arial, sans-serif; font-size: 13px; background-color: rgb(255, 255, 255); "><span >Optimization at IBM, in particular the two following topics:</span></span></div><div><span class="Apple-style-span" style="background-color: rgb(255, 255, 255); "><span style="font-family: arial, sans-serif; font-size: 13px; ">- Fine grained, constraint-level multi threading in CP solvers.</span><br /><span style="font-family: arial, sans-serif; font-size: 13px; ">- Just-in-time compilation techniques for CP solvers.</span></span></div><div><span class="Apple-style-span" style="background-color: rgb(255, 255, 255); "><span class="Apple-style-span" >For more info, contact him and/or consult this <a href="https://www.ibm.com/developerworks/university/phdfellowship/">page</a>.</span></span></div>pschaushttp://www.blogger.com/profile/10578391475922351456noreply@blogger.com0tag:blogger.com,1999:blog-3001120404365621770.post-15641611431378625332011-10-20T09:58:00.000-07:002011-10-20T10:00:02.866-07:002nd DHC to Pascal Van Hentenryck<div>After the University of Louvain it is now the university of Nantes that recognizes the contributions and impact of Pascal Van Hentenryck by confering him the title of Doctor Honoris Causa (more info <a href="http://www.univ-nantes.fr/1318604227748/0/fiche___actualite/&RH=COLL">here</a>).</div><div>This is always a good news for the visibility of CP. Congratulation to him!</div>pschaushttp://www.blogger.com/profile/10578391475922351456noreply@blogger.com0tag:blogger.com,1999:blog-3001120404365621770.post-49759610272231714692011-10-06T09:23:00.000-07:002011-10-06T09:23:17.320-07:00CP solves 99% of the problemsLaurent Perron gave an interesting talk at CP'11. Laurent was in charge of ILOG CP Opt and he is now at Google developping the OR department. During his talk he made this remark: "ILOG CP was an expensive product, thus we had only complex problems that were very difficult to solve. When a product costs a lot of money then the companies are interested in it only when they have a very complex (and difficult) problems. Or-tools (the Google CP Solver) is mainly used in internal by Googlers and most of the time for solving easy problems. Almost all problems that we solve everyday are easy." I also remember that Laurent explained to me that he received requests for solving "simple" questions like : enumerate all the possible combinations of these variables. If you need to write such a code from scratch this is not an easy task at all. In fact, some people would like to have a simple tool for writing things like "for each combination of values in this array satisfying this constraint do something". In this case CP is really a good answer.<br />
So maybe the answer about the problems solved by CP is the one proposed by Laurent and that is verified at Google: 99% of the real life problems arising everywhere :-)Jean-Charles Réginhttp://www.blogger.com/profile/06540516780781311246noreply@blogger.com1tag:blogger.com,1999:blog-3001120404365621770.post-37187192587265995592011-09-22T05:05:00.000-07:002011-09-22T05:23:35.298-07:00The sailing experience with CP<div>This is a very nice blog post written by Nathan Brixius <a href="http://nathanbrixius.wordpress.com/2011/09/21/shipbuilders-sailors-and-passengers/">here</a>. He compares the persons who build solvers to shipbuilder, people who write models to sailors and the end user of applications to passengers. The problem with CP is that the boat is so difficult to sail that to be a good sailor, you also need to have a very good knowledge in shipbuilding so I'm not sure the comparison holds for CP.</div><div>My opinions is that CP is probably more like a formula one. Very cool, very fast but .... don't tell me that Michael Schumacher doesn't know anything about the internals of his car (the only problem is that there is no place for passengers in a formula one ;-)).<br /></div>pschaushttp://www.blogger.com/profile/10578391475922351456noreply@blogger.com2tag:blogger.com,1999:blog-3001120404365621770.post-14253911357717476582011-09-05T00:17:00.000-07:002011-09-05T00:19:36.932-07:00The CP summer MercattoAfter Philippe Gilbert (cycling) joining BMC Racing Team and Romelu Lukaku (soccer) joining Chelsea another great Belgian transfer happened during the summer mercato.
<br />Leading computer scientist Pascal Van Hentenryck joins NICTA. This is a very good news for the field of CP that people like that will work together. More details in the <a href="http://www.prwire.com.au/pr/24724/leading-computer-scientist-pascal-van-hentenryck-joins-nicta">press release. </a>pschaushttp://www.blogger.com/profile/10578391475922351456noreply@blogger.com0tag:blogger.com,1999:blog-3001120404365621770.post-33187848285701153672011-07-03T05:24:00.000-07:002011-07-03T06:58:38.167-07:00RAII and backtrackingA conventional wisdom is that C++ is a powerful language but difficult to use and that could be unsafe. In fact, this is wrong. Only some languages like C++ may lead to safe applications.<br />
Why? This is mainly due to RAII. RAII means Resource Acquisition Is Initialization. You can have a look at Wikipedia.<br />
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Here is the idea. Consider a mechanism that is mainly implemented thanks to two opposite actions. For instance, you want to manage a file: you need to open and to close it. You want to manage resources: you will need to acquire and to release the resources. You need to manage the memory: you need to allocate and to deallocate the memory. <br />
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Now, imagine that a problem can happen in your program and you would like to be able to manage it. In other words, you have a normal code and a problem occurs. You need to catch it and to continue the program in a safe way. The main issue is that you need to abandon some current process before applying the second action of your mechanism. For instance, you need to close the files or release the resource you take. The main difficulty is that the error may happen anywhere in the program, so it is not easy to know what are the open files, the required resources... and how to access to this data.<br />
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C++ offers a nice way to deal with such a problem: you can easily respect the RAII principle which is "the object which performs the first action also performs the second one". In addition, the first action is performed in the constructor and the second one in the destructor. If a problem occurs then an exception is triggered and the execution goes back until a catch is found. The advantage of C++ is that all the destructors of the objects that are no longer valid will be called. Therefore, the files that have been opened will be closed, the resources will be release and so on... In addition, this will automatically be performed, so you don't have to be worried about it.<br />
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You can't do that in Java, because there is no real equivalent to destructor. There is no guarantee that the finalize function will be called and there is no guarantee about the order along with they will be called. <br />
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This is a strong advantage for C++. <br />
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C# has been recently modified for this reason.<br />
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Ok, but what is the relation with CP?<br />
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In CP we have to manage the wipeout event (the failure), that is when an inconsistent state is met. This happens when a domain is emptied for instance. In this case, the current state is inconsistent and we need to stop it immediately. Thus, we are face to the problem I explained. This problem involves all the local objects that have been defined or also the memory management.<br />
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There are usually 3 ways to deal with this in your code:<br />
- You use C++ and exceptions. Unfortunately, exception is a slow mechanism<br />
- You use C++ and setjmp/longjmp. Setjmp is faster than exception. However, it is not C++ compliant because the destructors are not called. This method is used in a lot of Solvers (like Gecode or or-tools), mainly because it is fast. Unfortunately this does not respect the RAII principle. You will have to manage by hand some part of the code.<br />
ILOG Solver did not recommend to use destructor and mentioned that destructor would not be called for object allocated on the solver heap. Maybe, this is the reason...<br />
- You deal with a lot of test. So, you add a lot of "if" in your code to make sure that there is no failure that happens. Unfortunately, you do not respect the RAII principles...<br />
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Hence, it seems that there is no perfect solution.<br />
In fact, there is a fourth solution, better than the previous ones and almost perfect, but I keep it for me :-)Jean-Charles Réginhttp://www.blogger.com/profile/06540516780781311246noreply@blogger.com3tag:blogger.com,1999:blog-3001120404365621770.post-3770805418286462232011-07-01T05:47:00.000-07:002011-07-01T05:50:11.344-07:00List of accepted papers to CP2011 is out<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhiy-bYaQijqpb-8UWvbkzlbXH_3vqiRu6ShodLCZg1nXSrCO2-tAhgW4q7piRHpQDIPOT5loWd7JQKKpQqZ1_EWVYq_nNOoBEy4r1RedzJYPelj3LbXtTM0N5k-2dTRIxGiTwWPw1SR70/s1600/logo_cp.png"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 245px; height: 105px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhiy-bYaQijqpb-8UWvbkzlbXH_3vqiRu6ShodLCZg1nXSrCO2-tAhgW4q7piRHpQDIPOT5loWd7JQKKpQqZ1_EWVYq_nNOoBEy4r1RedzJYPelj3LbXtTM0N5k-2dTRIxGiTwWPw1SR70/s320/logo_cp.png" border="0" alt=""id="BLOGGER_PHOTO_ID_5624365179338728994" /></a><br /><br /><br />This conference is the main international conference on the subject of constraint programming. The list of accepted papes is available <a href="http://www.dmi.unipg.it/cp2011/accepted_papers.html">here</a>.pschaushttp://www.blogger.com/profile/10578391475922351456noreply@blogger.com0