An efficient implementation of Edmonds'' maximum matching algorithm.

Authors:
Harold N. Gabow
Affiliations:
-
Venue:
An efficient implementation of Edmonds'' maximum matching algorithm.
Year:
1972

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An Efficient Implementation of Edmonds' Algorithm for Maximum Matching on Graphs

Journal of the ACM (JACM)
Testing graph connectivity

STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing

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Abstract

A matching in a graph is a collection of edges, no two of which share a vertex. A maximum matching contains the greatest number of edges possible. This paper presents an efficient implementation of Edmonds'' algorithm for finding maximum matchings. The computation time is proportional to $V^3$, where V is the number of vertices; previous algorithms have computation time proportional to $V^4$. The implementation avoids Edmonds'' blossom reduction by using pointers to encode the structure of alternating paths.