Elsevier

Information Processing Letters

Volume 84, Issue 4, 30 November 2002, Pages 189-193
Information Processing Letters

A simple matching algorithm for regular bipartite graphs

https://doi.org/10.1016/S0020-0190(02)00273-9Get rights and content

Abstract

We consider the perfect matching problem for a Δ-regular bipartite graph with n vertices and m edges, i.e., 12nΔ=m, and present a new O(m+nlognlogΔ) algorithm. Cole and Rizzi, respectively, gave algorithms of the same complexity as ours, Schrijver also devised an O() algorithm, and the best existing algorithm is Cole, Ost, and Schirra's O(m) algorithm. Extending Gabow's perfect matching algorithm for 2t-regular bipartite graph with a positive integer t and using Cole and Hopcroft's edge-sparsification technique, we show another approach to the perfect matching problem, which results in a simple algorithm that employs no sophisticated data structure such as dynamic tree and splay tree.

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This work was supported in part by Grants-in-Aid for Scientific Research by the Ministry of Education, Science, Sports, Culture and Technology of Japan.

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