We make several observations on the implementation of Edmonds' blossom algorithm for solving minimum-weight perfect-matching problems and we present computational results for geometric problem instances ranging in size from 1,000 nodes up to 5,000,000 nodes. A key feature in our implementation is the use of multiple search trees with an individual dual-change " for each tree. As a benchmark of the algorithm's performance, solving a 100,000 node geometric instance on a 200 Mhz Pentium-Pro computer takes approximately 3 minutes. A perfect matching in a graph G is a subset of edges such that each node in G is met by exactly one edge in the subset. Given a real weight c e for each edge e of G, the minimumweight perfect-matching problem is to find a perfect matching M of minimum weight P (c e : e 2 M ). One of the fundamental results in combinatorial optimization is the polynomialtime blossom algorithm for computing minimum-weight perfect matchings by Edmonds [22, 23]. This algori...
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