A scaling algorithm for maximum weight matching in bipartite graphs

Authors:
Ran Duan;Hsin-Hao Su
Affiliations:
University of Michigan;University of Michigan
Venue:
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Year:
2012

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Abstract

Given a weighted bipartite graph, the maximum weight matching (MWM) problem is to find a set of vertex-disjoint edges with maximum weight. We present a new scaling algorithm that runs in O(m√n log N) time, when the weights are integers within the range of [0,N]. The result improves the previous bounds of O(Nm√n) by Gabow and O(m√n log (nN)) by Gabow and Tarjan over 20 years ago. Our improvement draws ideas from a not widely known result, the primal method by Balinski and Gomory.