Heuristic initialization for bipartite matching problems

Abstract

It is a well-established result that improved pivoting in linear solvers can be achieved by computing a bipartite matching between matrix entries and positions on the main diagonal. With the availability of increasingly faster linear solvers, the speed of bipartite matching computations must keep up to avoid slowing down the main computation. Fast algorithms for bipartite matching, which are usually initialized with simple heuristics, have been known for a long time. However, the performance of these algorithms is largely dependent on the quality of the heuristic. We compare combinations of several known heuristics and exact algorithms to find fast combined methods, using real-world matrices as well as randomly generated instances. In addition, we present a new heuristic aimed at obtaining high-quality matchings and compare its impact on bipartite matching algorithms with that of other heuristics. The experiments suggest that its performance compares favorably to the best-known heuristics, and that it is especially suited for application in linear solvers.