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(N m √ 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.
Duan and Su REF recently found a weight-scaling algorithm for this max-weight matching problem that runs in time O(m √ n log C).
A Scaling Algorithm for Maximum Weight Matchings in Bipartite Graphs
In 23rd SODA
Mathematics Computer Science