Abstract
Previous chapter Next chapter Full AccessProceedings Proceedings of the 2012 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)Efficient Algorithms for Maximum Weight Matchings in General Graphs with Small Edge WeightsChien-Chung Huang and Telikepalli KavithaChien-Chung Huang and Telikepalli Kavithapp.1400 - 1412Chapter DOI:https://doi.org/10.1137/1.9781611973099.110PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstract Let G = (V, E) be a graph with positive integral edge weights. Our problem is to find a matching of maximum weight in G. We present a simple iterative algorithm for this problem that uses a maximum cardinality matching algorithm as a subroutine. Using the current fastest maximum cardinality matching algorithms, we solve the maximum weight matching problem in O(W√nm logn(n2/m)) time, or in O(W nω) time with high probability, where n = |V|, m = |E|, W is the largest edge weight, and ω < 2.376 is the exponent of matrix multiplication. In relatively dense graphs, our algorithm performs better than all existing algorithms with W = o(log1.5 n). Our technique hinges on exploiting Edmonds’ matching polytope and its dual. Previous chapter Next chapter RelatedDetails Published:2012ISBN:978-1-61197-210-8eISBN:978-1-61197-309-9 https://doi.org/10.1137/1.9781611973099Book Series Name:ProceedingsBook Code:PR141Book Pages:xiii + 1757
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