Tutte Colloquium - Seth Pettie

Title: Weighted matching on general graphs: faster and simpler

Abstract: We present a new scaling algorithm for maximum (or minimum) weight perfect matching on general, edge weighted graphs.  The algorithm runs in O(mn^{1/2}log(nW)) time, where m, n, and W are the numbers of edges, vertices and maximum integer edge weight.  This bound matches the fastest algorithm for bipartite graphs and comes within a log(nW) factor of the Micali-Vazirani cardinality matching algorithm. In terms of running time our algorithm is just slightly faster than the previous best (Gabow and Tarjan, 1991) by a roughly (log n)^{1/2} factor.  However, it is dramatically simpler to describe and analyze.