New Iterative Algorithms for Weighted Matching

Abstract

Matching is an important combinatorial problem with a number ofpractical applications. Even though there exist polynomial time solutionsto most matching problems, there are settings where these are too slow.This has led to the development of several fast approximation algorithmsthat in practice compute matchings very close to the optimal.The current paper introduces a new deterministic approximationalgorithm named G 3 , for weighted matching. The algorithm is based ontwo main ideas, the first is to compute heavy subgraphs of the originalgraph on which we can compute optimal matchings. The second idea isto repeatedly merge these matchings into new matchings of even higherweight than the original ones. Both of these steps are achieved usingdynamic programming in linear or close to linear time.We compare G 3 with the randomized algorithm GPA+ROMA whichis the best known algorithm for this problem. Experiments on alarge collection of graphs show that G 3 is substantially faster thanGPA+ROMA while computing matchings of comparable weight