New Algorithms for Maximum Weight Matching and a Decomposition Theorem

Chien-Chung Huang () and Telikepalli Kavitha ()
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Chien-Chung Huang: Chalmers University of Technology
Telikepalli Kavitha: Tata Institute of Fundamental Research, India

Mathematics of Operations Research, 2017, vol. 42, issue 2, 411-426

Abstract: We revisit the classical maximum weight matching problem in general graphs with nonnegative integral edge weights. We present an algorithm that operates by decomposing the problem into W unweighted versions of the problem, where W is the largest edge weight. Our algorithm has running time as good as the current fastest algorithms for the maximum weight matching problem when W is small. One of the highlights of our algorithm is that it also produces an integral optimal dual solution; thus our algorithm also returns an integral certificate corresponding to the maximum weight matching that was computed. Our algorithm yields a new proof to the total dual integrality of Edmonds’ matching polytope and it also gives rise to a decomposition theorem for the maximum weight of a matching in terms of the maximum size of a matching in certain subgraphs. We also consider the maximum weight capacitated b -matching problem in bipartite graphs with nonnegative integral edge weights and show that it can also be decomposed into W unweighted versions of the problem, where W is the largest edge weight. Our second algorithm is competitive with known algorithms when W is small.

Keywords: maximum weight matching; exact algorithms; total dual integrality (search for similar items in EconPapers)
Date: 2017
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