https://curiouscoding.nl/tags/ilp/Recent content in Ilp on CuriousCodingHugoenThu, 05 Sep 2024 00:00:00 +0200https://curiouscoding.nl/posts/pace24/Thu, 05 Sep 2024 00:00:00 +0200https://curiouscoding.nl/posts/pace24/<div class="ox-hugo-toc toc has-section-numbers"> <div class="heading">Table of Contents</div> <ul> <li><span class="section-num">1</span> <a href="#general-observations" >General observations</a></li> <li><span class="section-num">2</span> <a href="#heuristic-track" >Heuristic track</a></li> <li><span class="section-num">3</span> <a href="#parameterized-track" >Parameterized track</a></li> <li><span class="section-num">4</span> <a href="#exact-track" >Exact track</a></li> </ul> </div> <!--endtoc--> <p>In this post I will collect some high level ideas and approaches used to solve the PACE 2024 challenge. Very briefly, the goal is to write fast solvers for NP-hard problems. The problem for the <a href="https://pacechallenge.org/2024/" class="external-link" target="_blank" rel="noopener">2024 edition is one-side crossing minimization</a>: Given is a bipartite graph \((A, B)\) that is drawn in standard way with the nodes of both \(A\) and \(B\) on a line, where the order of the nodes of \(A\) is fixed. The goal is to find a permutation of \(B\) that minimizes the number of edge crossings when all edges are drawn as straight lines.</p>