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A primal algorithm for optimum matching

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Polyhedral Combinatorics

Part of the book series: Mathematical Programming Studies ((MATHPROGRAMM,volume 8))

Abstract

An algorithm for finding an optimum weight perfect matching in a graph is described. It differs from Edmonds’ “blossom” algorithm in that a perfect matching is at hand throughout the algorithm, and a feasible solution to the dual problem is obtained only at termination. In many other respects, including its efficiency, it is similar to the blossom algorithm. Some advantages of this “primal” algorithm for certain post-optimality problems are described. The algorithm is used to prove that, if the weights are integers, then the dual problem has an optimal solution which is integer-valued. Finally, some graph-theoretic results on perfect matchings are derived.

Research was done while this author was with the Department of Mathematical Sciences, Johns Hopkins University, and was supported in part by National Science Foundation Grant MCS76-08803.

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Author information

Authors and Affiliations

  1. Carleton University, Ottawa, Canada

    W. H. Cunningham

  2. The Johns Hopkins University, Baltimore, MD, U.S.A

    A. B. Marsh

Authors
  1. W. H. Cunningham
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  2. A. B. Marsh
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Editor information

M. L. Balinski A. J. Hoffman

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Dedicated to the memory of D. Ray Fulkerson

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© 1978 The Mathematical Programming Society

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Cunningham, W.H., Marsh, A.B. (1978). A primal algorithm for optimum matching. In: Balinski, M.L., Hoffman, A.J. (eds) Polyhedral Combinatorics. Mathematical Programming Studies, vol 8. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0121194

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  • DOI: https://doi.org/10.1007/BFb0121194

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00789-7

  • Online ISBN: 978-3-642-00790-3

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