Experiments on push-relabel-based maximum cardinality matching algorithms for bipartite graphs

Kamer Kaya, Johannes Langguth, Fredrik Manne, and Bora Uçar

Abstract. We report on careful implementations of several push-relabel-based algorithms for solving the problem of finding a maximum cardinality matching in a bipartite graph and compare them with fast augmenting- path-based algorithms. We analyze the algorithms using a common base for all implementations and compare their relative performance and stability on a wide range of graphs. The effect of a set of known initialization heuristics on the performance of matching algorithms is also investigated. Our results identify a variant of the push-relabel algorithm and a variant of the augmenting-path-based algorithm as the fastest with proper initialization heuristics, while the push-relabel based one having a better worst case performance.

Key words. Bipartite graphs, matching, push-relabel