Computing Minimum-Weight Perfect Matchings

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.