Martin Koutecký | Homepage @ Technionhttp://research.koutecky.name/2018-04-25T11:30:00+02:00Talk—Elections, Bribery, and Integer Programming2018-04-25T11:30:00+02:002018-04-25T11:30:00+02:00Martin Kouteckýtag:research.koutecky.name,2018-04-25:talk-telaviv-april2018.html<p>A former postdoc of my current advisor Shmuel Onn, Antoine Deza, organized a very nice workshop on <a class="reference external" href="http://www.cas.mcmaster.ca/~deza/tau2018.html">Optimization and Discrete Geometry : Theory and Practice</a>.
I was very happy to give a talk where I tried to explain how our recent breakthroughs in computational social choice come from making connections to discrete geometry and integer programming.</p>
<p>First, we take a distinctly geometric viewpoint on elections, voting and bribery (<a class="reference external" href="https://arxiv.org/abs/1801.09584">paper</a>).
One implication is for example that we now see that the different computational complexity of bribery with respect to different voting rules is reflected in the <em>geometric descriptive complexity</em> of the set of societies where our preferred candidate wins:</p>
<ul class="simple">
<li>For scoring protocols and Condorcet's rule, this set is a convex set,</li>
<li>For Copeland and many others it is a disjunction of convex sets, or, equivalently, the set of integer points of a <em>projection</em> of a convex sets,</li>
<li>For Dodgson and Young it is a set given by a <span class="formula">∀∃</span> quantifier alternation, that is, much more complex than the above.</li>
</ul>
<p>Second, we observe that the original ILP (going back to the work of Bartholdi-Tovey-Trick from 1989) has a very special <span class="formula"><i>n</i></span>-fold format, and we develop faster algorithms for ILPs of this form, thus speeding up existing algorithms significantly (<a class="reference external" href="https://arxiv.org/abs/1705.08657">paper</a>).
Intuitively, our algorithm works as follows.
We start with some trivial bribery which makes our candidate win, but is too expensive.
A key lemma says that if the current bribery is <em>not optimal</em>, then only a small number of voters need to be modified to obtain a cheaper bribery.
Such a small <em>augmenting step</em> can then be found using dynamic programming, and repeatedly augmenting eventually brings us to the optimal solution.</p>
<p>Third, there's a few ideas about how to model more complex campaigning and where this gets stuck (currently). If you have any ideas on how to get <em>unstuck</em>, please email me, I'll be happy to collaborate!</p>
<p><a class="reference external" href="../../talks/talk_telaviv_april2018.pdf">Slides</a>.</p>
Talk—Integer Programming: Techniques & Applications2018-03-27T13:00:00+02:002018-03-27T13:00:00+02:00Martin Kouteckýtag:research.koutecky.name,2018-03-27:talk-prague-spring2018.html<p>I went to Prague to give a talk which summarizes a big chunk of my research in the past 2 years.
The topics covered are:</p>
<ul class="simple">
<li>Integer Programming (IP) in general</li>
<li>Brief mention of fixed dimension theory of IP</li>
<li>Unifying theory of IP in variable dimension (capturing basically all developments since total unimodularity) (<a class="reference external" href="https://arxiv.org/abs/1802.05859">paper</a>)</li>
<li>Applications to Computational Social Choice (elections, voting, bribing, etc.) (<a class="reference external" href="https://arxiv.org/abs/1705.08657">speed-ups</a>, <a class="reference external" href="https://arxiv.org/abs/1801.09584">new model + handling complex voting rules</a>, diffusion model - available soon)</li>
<li>Some experimental results of the IP tools we developed. (<a class="reference external" href="https://arxiv.org/abs/1802.09007">paper</a>)</li>
</ul>
<p><a class="reference external" href="../../talks/talk_prague_spring2018.pdf">Slides</a>.</p>
Blog start2015-08-04T14:00:00+02:002015-08-04T14:00:00+02:00Martin Kouteckýtag:research.koutecky.name,2015-08-04:blog-start.html<p>Possibly, something will appear here when I have a) something worthwhile
to write about my research, b) the time to do so. At the time, I
possess neither.</p>