Scaling algorithms for weighted matching in general graphs

Abstract

We present a new scaling algorithm for maximum (or minimum) weight perfect matching on general, edge weighted graphs. Our algorithm runs in O(m p n log(nN)) time, O(m p n) per scale, which matches the running time of the best cardinality matching algorithms on sparse graphs [29, 18]. Here m; n; and N bound the number of edges, vertices, and magnitude of any integer edge weight. Our result improves on a 25-year old algorithm of Gabow and Tarjan, which runs in O(m √ n log n (m; n) log(nN)) time.