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Optimum matching forests II: General weights

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Abstract

Matching forests generalize branchings in a directed graph and matchings in an undirected graph. We present an efficient algorithm, the PMF Algorithm, for the problem: given a mixed graphG and a real weight on each of its edges, find a perfect matching forest of maximum weight-sum. The PMF Algorithm proves the sufficiency of a linear system which definesP = (G) andP(G), the convex hull of incidence vectors of perfect matching forests and matching forests respectively ofG. The algorithm also provides a generalization of Tutte's theorem on the existence of perfect matchings in an undirected graph.

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Authors and Affiliations

  1. Department of Mathematics, University of Kentucky, 40506, Lexington, KY, USA

    Rick Giles

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  1. Rick Giles
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Additional information

Research partially supported by a N.R.C. of Canada Postdoctorate Fellowship.

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Giles, R. Optimum matching forests II: General weights. Mathematical Programming 22, 12–38 (1982). https://doi.org/10.1007/BF01581023

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  • DOI: https://doi.org/10.1007/BF01581023

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