On Parallel Push-Relabel based Algorithms for Bipartite Maximum Matching

Journal Article · Tue Jul 01 04:00:00 EDT 2014 · Parallel Computing, 40(7):289 - 308

DOI:https://doi.org/10.1016/j.parco.2014.03.004· OSTI ID:1171882

Langguth, Johannes; Azad, Md Ariful; Halappanavar, Mahantesh; Manne, Fredrik

We study multithreaded push-relabel based algorithms for computing maximum cardinality matching in bipartite graphs. Matching is a fundamental combinatorial (graph) problem with applications in a wide variety of problems in science and engineering. We are motivated by its use in the context of sparse linear solvers for computing maximum transversal of a matrix. We implement and test our algorithms on several multi-socket multicore systems and compare their performance to state-of-the-art augmenting path-based serial and parallel algorithms using a testset comprised of a wide range of real-world instances. Building on several heuristics for enhancing performance, we demonstrate good scaling for the parallel push-relabel algorithm. We show that it is comparable to the best augmenting path-based algorithms for bipartite matching. To the best of our knowledge, this is the first extensive study of multithreaded push-relabel based algorithms. In addition to a direct impact on the applications using matching, the proposed algorithmic techniques can be extended to preflow-push based algorithms for computing maximum flow in graphs.

• Research Organization: Pacific Northwest National Laboratory (PNNL), Richland, WA (US)
• Sponsoring Organization: USDOE
• DOE Contract Number: AC05-76RL01830
• OSTI ID: 1171882
• Report Number(s): PNNL-SA-91913; 400470000
• Journal Information: Parallel Computing, 40(7):289 - 308, Journal Name: Parallel Computing, 40(7):289 - 308
• Country of Publication: United States
• Language: English

Related Subjects

Push-relabel
matching
bipartite