New Algorithms for Maximum Weight Matching and a Decomposition Theorem

• 成果类型: Article
• 署名作者: Huang, Chien-Chung; Kavitha, Telikepalli
• 署名单位: Chalmers University of Technology; Tata Institute of Fundamental Research (TIFR)
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2016.0806
• 发表日期: 2017
• 页码: 411-426
• 关键词: faster scaling algorithms

摘要

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.