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Maximum Matching

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Encyclopedia of Algorithms

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Years and Authors of Summarized Original Work

2004; Mucha, Sankowski

Problem Definition

Let G = (V, E) be an undirected graph, and let \(n =\vert V \vert\), \(m =\vert E\vert\). A matching in G is a subset M ⊆ E, such that no two edges of M have a common endpoint. A perfect matching is a matching of cardinality n∕2. The most basic matching related problems are finding a maximum matching (i.e., a matching of maximum size) and, as a special case, finding a perfect matching if one exists. One can also consider the case where a weight function w : E → R is given and the problem is to find a maximum weight matching.

The maximum matching and maximum weight matching are two of the most fundamental algorithmic graph problems. They have also played a major role in the development of combinatorial optimization and algorithmics. An excellent account of this can be found in a classic monograph [11] by Lovász and Plummer devoted entirely to matching problems. A more up-to-date but also more...

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Recommended Reading

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Authors and Affiliations

  1. Faculty of Mathematics, Informatics and Mechanics, Institute of Informatics, Warsaw, Poland

    Marcin Mucha

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  1. Marcin Mucha
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Correspondence to Marcin Mucha .

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Editors and Affiliations

  1. Dept. Electrical Engineering & Computer Science, Northwestern University, Evanston, Illinois, USA

    Ming-Yang Kao

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Mucha, M. (2015). Maximum Matching. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-3-642-27848-8_225-2

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  • DOI: https://doi.org/10.1007/978-3-642-27848-8_225-2

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  • Online ISBN: 978-3-642-27848-8

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