NDLI: A Decomposition Theorem for Maximum Weight Bipartite Matchings

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Kao, Ming-Yang Sung, Wing-Kin Ting, Hing-Fung Lam, Tak-Wah
Copyright Year	2001
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 (x2 /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.
Starting Page	18
Ending Page	26
Page Count	9
File Format	PDF
ISSN	00975397
DOI	10.1137/S0097539799361208
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	1
Volume Number	31
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-27
Access Restriction	Subscribed
Subject Keyword	Trees maximum weight matchings Analysis of algorithms and problem complexity Factorization, matching, partitioning, covering and packing unfolded graphs minimum weight covers Graph algorithms all-cavity matchings graph algorithms
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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