A Bidirectional GPU Algorithm for Computing Maximum Matchings in Bipartite Graphs

Computing maximum matchings in bipartite graphs is an important problem with applications in domains such as resource allocation, chemical analysis, and bioinformatics. The leading algorithms for this computation follow an augmenting-path-based approach. Since they involve traversing and propagating information along long paths, it is challenging to extract large amounts of parallelism from them. Moreover, the synchronization requirement is high as the threads must maintain vertex-disjoint paths. We present a novel GPU algorithm called ECL-MM that exposes more parallelism, minimizes synchronization, and reduces path overlaps. It includes a new parallel algorithm for quickly finding an initial maximal matching for starting the augmenting-path computation. Our results from an RTX-4090 GPU show that ECL-MM outperforms the fastest prior multicore CPU code by a factor of 4.5 and the fastest prior GPU code by a factor of $\mathbf{1. 6 3}$.