Enhanced Approximation Algorithms for Maximum Weight Matchings of Graphs

摘要

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(EVlogV) 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.