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2018 Proceedings of the Seventh SIAM Workshop on Combinatorial Scientific Computing

Approximation algorithms for maximum matchings in undirected graphs

Abstract

We propose heuristics for approximating the maximum cardinality matching on undirected graphs. Our heuristics are based on the theoretical body of a certain type of random graphs, and are made practical for real-life ones. The idea is based on judiciously selecting a subgraph of a given graph and obtaining a maximum cardinality matching on this subgraph. We show that the heuristics have an approximation guarantee of around 0.866 — log(n)/n for a graph with n vertices. Experiments for verifying the theoretical results in practice are provided.

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cover image Proceedings
2018 Proceedings of the Seventh SIAM Workshop on Combinatorial Scientific Computing
Pages: 56 - 65
Editors: Fredrik Manne, University of Bergen, Norway, Peter Sanders, Karlsruhe Institute of Technology, Germany, and Sivan Toledo, Tel-Aviv University, Israel
ISBN (Online): 978-1-61197-521-5

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Published online: 7 August 2018

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