Weighted Matching

  • Bernhard Korte
  • Jens Vygen
Part of the Algorithms and Combinatorics book series (AC, volume 21)


Nonbipartite weighted matching appears to be one of the “hardest” combinatorial optimization problems that can be solved in polynomial time. We shall extend EDMONDS ’ CARDINALITY MATCHING ALGORITHM to the weighted case and shall again obtain an O(n3)-implementation. This algorithm has many applications, some of which are mentioned in the exercises and in Section  12.2.


General Literature

  1. Gerards, A.M.H. [1995]: Matching. In: Handbooks in Operations Research and Management Science; Volume 7: Network Models (M.O. Ball, T.L. Magnanti, C.L. Monma, G.L. Nemhauser, eds.), Elsevier, Amsterdam 1995, pp. 135–224Google Scholar
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  4. Pulleyblank, W.R. [1995]: Matchings and extensions. In: Handbook of Combinatorics; Vol. 1 (R.L. Graham, M. Grötschel, L. Lovász, eds.), Elsevier, Amsterdam 1995Google Scholar

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Copyright information

© Springer-Verlag GmbH Germany 2018

Authors and Affiliations

  • Bernhard Korte
    • 1
  • Jens Vygen
    • 1
  1. 1.Research Institute for Discrete MathematicsUniversity of BonnBonnGermany

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