We make several observations on the implementation of Edmonds’ blossom algorithm for solving minimum-weight perfectmatching 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.

Abstract not found

We describe the implementation of an O(nm log n) algorithm for weighted matchings in general graphs. The algorithm is a variant of the algorithm of Galil, Micali, and Gabow [GMG86] and requires the use of concatenable priority queues. No previous implementation had a worst{case guarantee of O(nm log n). We compare our implementation to the experimentally fastest implementation (called Blossom IV) due to Cook and Rohe [CR97]; Blossom IV is an implementation of Edmonds' algorithm and has a running time no better than (n 3 ). Blossom IV requires only very simple data structures. Our experiments show that our new implementation is competitive to Blossom IV. 1