A Decomposition Theorem for Maximum Weight Bipartite Matchings
Abstract
Let G be a bipartite graph with positive integer weights on the edges and without isolated nodes. Let n, N and W be the node count, the largest edge weight and the total weight of G. Let k(x,y) be log(x)/log(x^2/y). We present a new decomposition theorem for maximum weight bipartite matchings and use it to design an O(sqrt(n)W/k(n,W/N))-time algorithm for computing a maximum weight matching of G. This algorithm bridges a long-standing gap between the best known time complexity of computing a maximum weight matching and that of computing a maximum cardinality matching. Given G and a maximum weight matching of G, we can further compute the weight of a maximum weight matching of G-{u} for all nodes u in O(W) time.
Cite
@article{arxiv.cs/0011015,
title = {A Decomposition Theorem for Maximum Weight Bipartite Matchings},
author = {Ming-Yang Kao and Tak-Wah Lam and Wing-Kin Sung and Hing-Fung Ting},
journal= {arXiv preprint arXiv:cs/0011015},
year = {2007}
}
Comments
The journal version will appear in SIAM Journal on Computing. The conference version appeared in ESA 1999