Weighted Matching on General Graphs: Faster and Simpler

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.

Joint work with Ran Duan (IIIS, Tsinghua) and Hsin-Hao Su (MIT).
Manuscript available at http://arxiv.org/abs/1411.1919v2.