New Approximation Algorithms for the Weighted Matching Problem

Finding matchings of maximum weight is a classical problem in combinatorial optimization. The fastest algorithm known today for solving this problem has running time O(mn+n log n). Several applications require algorithms for the weighted matching problem with better running time. Up to now no algorithm with o(mn) running time was known that achieves an approximation ratio better than 2 3 . We present two approximation algorithms for the weighted matching problem in graphs with an approximation ratio of 3 4 − ǫ respectively 4 5 − ǫ and running time O(m log n) respectively O(m log n).

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