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="https://fatcat.wiki/container/7dys7zoberdktmxyjciuy5bnse" 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.
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