Matching: A Well-Solved Class of Integer Linear Programs

  • Jack Edmonds
  • Ellis L. Johnson

Abstract

A main purpose of this work is to give a good algorithm for a certain well-described class of integer linear programming problems, called matching problems (or the matching problem). Methods developed for simple matching [2]

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Berge, C., Théorie des graphes et ses applications, Dunod, Paris, 1958.Google Scholar
  2. 2.
    Edmonds, J., Paths, trees, and flowers, Canad. J. Math. 17 (1965), 449–467.MathSciNetMATHGoogle Scholar
  3. 3.
    Edmonds, J., Maximum matching and a polyhedron with 0,1-vertices, J. Res. Nat. Bur. Standards 69B (1965), 125–130.MathSciNetGoogle Scholar
  4. 4.
    Edmonds, J., An introduction to matching, preprinted lectures, Univ. of Mich. Summer Engineering Conf. 1967.Google Scholar
  5. 5.
    Johnson, E.L., Programming in networks and graphs, Operation Research Center Report 65-1, Etchavary Hall, Univ. of Calif., Berkeley.Google Scholar
  6. 6.
    Tutte, W.T., The factorization of linear graphs, J. London Math. Soc. 22 (1947), 107–111.CrossRefMathSciNetMATHGoogle Scholar
  7. 7.
    Tutte, W.T., The factors of graphs, Canad. J. Math. 4 (1952), 314–328.MathSciNetMATHGoogle Scholar
  8. 8.
    Witzgall, C. and Zahn, C.T. Jr., Modification of Edmonds’ matching algorithm, J. Res. Nat. Bur. Standards 69B (1965), 91–98.MathSciNetGoogle Scholar
  9. 9.
    White, L.J., A parametric study of matchings, Ph.D. Thesis, Dept. of Elec. Engineering, Univ. of Mich., 1967.Google Scholar
  10. 10.
    Balinski, M., A labelling method for matching, Combinatorics Conference, Univ. of North Carolina, 1967.Google Scholar
  11. 11.
    Balinski, M., Establishing the matching poloytope, preprint, City Univ. of New York, 1969.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Jack Edmonds
    • 1
  • Ellis L. Johnson
    • 2
  1. 1.National Bureau of StandardsWashington, D.C.USA
  2. 2.I.B.M. Research CenterYorktown HeightsUSA

Personalised recommendations