Abstract
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(Wnω) time with high probability, where n = |V|, m = |E|, W is the largest edge weight, and ω
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