IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Online ISSN : 1745-1337
Print ISSN : 0916-8508
Special Section on Selected Papers from the 20th Workshop on Circuits and Systems in Karuizawa
Enhanced Approximation Algorithms for Maximum Weight Matchings of Graphs
Daisuke TAKAFUJISatoshi TAOKAYasunori NISHIKAWAToshimasa WATANABE
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Volume E91.A (2008) Issue 4 Pages 1129-1139

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Abstract

The subject of this paper is maximum weight matchings of graphs. An edge set M of a given graph G is called a matching if and only if any pair of edges in M share no endvertices. A maximum weight matching is a matching whose total weight (total sum of edge-weights) is maximum among those of G. The maximum weight matching problem (MWM for short) is to find a maximum weight matching of a given graph. Polynomial algorithms for finding an optimum solution to MWM have already been proposed: for example, an O(|V|4) time algorithm proposed by J. Edmonds, and an O(|E||V| log|V|) time algorithm proposed by H. N. Gabow. Some applications require obtaining a matching of large total weight (not necessarily a maximum one) in realistic computing time. These existing algorithms, however, spend extremely long computing time as the size of a given graph becomes large, and several fast approximation algorithms for MWM have been proposed. In this paper, we propose six approximation algorithms GRS+, GRS_F+, GRS_R+, GRS_S+, LAM_a+ and LAM_as+. They are enhanced from known approximation ones by adding some post-processings that consist of improved search of weight augmenting paths. Their performance is evaluated through results of computing experiment.

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© 2008 The Institute of Electronics, Information and Communication Engineers
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