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Enhanced Approximation Algorithms for Maximum Weight Matchings of Graphs
Daisuke TAKAFUJI Satoshi TAOKA Yasunori NISHIKAWA Toshimasa WATANABE
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E91A
No.4
pp.11291139 Publication Date: 2008/04/01
Online ISSN: 17451337 Print ISSN: 09168508 Type of Manuscript: Special Section PAPER (Special Section on Selected Papers from the 20th Workshop on Circuits and Systems in Karuizawa) Category: Keyword: the maximum weight matching problem of graphs, approximate solutions, weight augmenting paths,
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Summary:
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 edgeweights) 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(EVlog 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 postprocessings that consist of improved search of weight augmenting paths. Their performance is evaluated through results of computing experiment.

