Encyclopedia of Algorithms

2016 Edition
| Editors: Ming-Yang Kao

Assignment Problem

  • Samir Khuller
Reference work entry
DOI: https://doi.org/10.1007/978-1-4939-2864-4_35

Years and Authors of Summarized Original Work

  • 1955; Kuhn

  • 1957; Munkres

Problem Definition

Assume that a complete bipartite graph, G(X, Y, X × Y ), with weights w(x, y) assigned to every edge (x, y) is given. A matching M is a subset of edges so that no two edges in M have a common vertex. A perfect matching is one in which all the nodes are matched. Assume that \(\vert X\vert =\vert Y \vert = n\)


Weighted bipartite matching 
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Recommended Reading

  1. 1.
    Ahuja R, Magnanti T, Orlin J (1993) Network flows: theory, algorithms and applications. Prentice Hall, Englewood CliffszbMATHGoogle Scholar
  2. 2.
    Cook W, Cunningham W, Pulleyblank W, Schrijver A (1998) Combinatorial Optimization. Wiley, New YorkzbMATHGoogle Scholar
  3. 3.
    Gabow H (1990) Data structures for weighted matching and nearest common ancestors with linking. In: Symposium on discrete algorithms, San Francisco, pp 434–443zbMATHGoogle Scholar
  4. 4.
    Kuhn H (1955) The Hungarian method for the assignment problem. Naval Res Logist Q 2:83–97MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Lawler E (1976) Combinatorial optimization: networks and matroids. Holt, Rinehart and Winston, New YorkzbMATHGoogle Scholar
  6. 6.
    Munkres J (1957) Algorithms for the assignment and transportation problems. J Soc Ind Appl Math 5:32–38MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Computer Science DepartmentUniversity of MarylandCollege ParkUSA