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Bipartite matching heuristics with quality guarantees on shared memory parallel computers

Abstract : We propose two heuristics for the bipartite matching problem that are amenable to shared-memory parallelization. The first heuristic is very intriguing from parallelization perspective. It has no significant algorithmic synchronization overhead and no conflict resolution is needed across threads. We show that this heuristic has an approximation ratio of around 0.632. The second heuristic is designed to obtain a larger matching by employing the well-known Karp-Sipser heuristic on a judiciously chosen subgraph of the original graph. We show that the Karp-Sipser heuristic always finds a maximum cardinality matching in the chosen subgraph. Although the Karp-Sipser heuristic is hard to parallelize for general graphs, we exploit the structure of the selected subgraphs to propose a specialized implementation which demonstrates a very good scalability. Based on our experiments and theoretical evidence, we conjecture that this second heuristic obtains matchings with cardinality of at least 0.866 of the maximum cardinality. We discuss parallel implementations of the proposed heuristics on shared memory systems. Experimental results, for demonstrating speed-ups and verifying the theoretical results in practice, are provided.
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Submitted on : Monday, July 7, 2014 - 9:45:46 AM
Last modification on : Friday, November 18, 2022 - 9:28:35 AM
Long-term archiving on: : Tuesday, April 11, 2017 - 9:44:51 AM


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  • HAL Id : hal-00877211, version 3


Fanny Dufossé, Kamer Kaya, Bora Uçar. Bipartite matching heuristics with quality guarantees on shared memory parallel computers. [Research Report] Inria; laas. 2013, pp.28. ⟨hal-00877211v3⟩



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