Algebraic Algorithms for Matching and Matroid Problems

Nicholas J. A. Harvey
<span title="">2009</span> <i title="Society for Industrial &amp; Applied Mathematics (SIAM)"> <a target="_blank" rel="noopener" href="" style="color: black;">SIAM journal on computing (Print)</a> </i> &nbsp;
We present new algebraic approaches for two well-known combinatorial problems: non-bipartite matching and matroid intersection. Our work yields new randomized algorithms that exceed or match the efficiency of existing algorithms. For nonbipartite matching, we obtain a simple, purely algebraic algorithm with running time O(n ω ) where n is the number of vertices and ω is the matrix multiplication exponent. This resolves the central open problem of Mucha and Sankowski (2004) . For matroid
more &raquo; ... tion, our algorithm has running time O(nr ω−1 ) for matroids with n elements and rank r that satisfy some natural conditions.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="">doi:10.1137/070684008</a> <a target="_blank" rel="external noopener" href="">fatcat:ksxiwohxxvdvddo3xq4wabw2lq</a> </span>
<a target="_blank" rel="noopener" href="" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href=""> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / </button> </a>