Advertisement

Mathematical Programming

, Volume 38, Issue 2, pp 147–159 | Cite as

Greedy algorithm and symmetric matroids

  • André Bouchet
Article

Abstract

Symmetric matroids are set systems which are obtained, in some sense, by a weakening of the structure of a matroid. These set systems are characterized by a greedy algorithm and they are suitable for dealing with autodual properties of matroids. Applications are given to the eulerian tours of 4-regular graphs and the theory ofg-matroids.

Key words

Matroid greedy algorithm Euler tour 4-regular graph 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    A. Bouchet, “Isotropic systems,” to appear inEuropean Journal of Combinatorics.Google Scholar
  2. [2]
    A. Bouchet, “Graphic presentations of isotropic systems,” submitted.Google Scholar
  3. [3]
    D. Gale, “Optimal assignments in an ordered set: an application of matroid theory,”Journal of Combinatorial Theory 4 (1968) 176–180.zbMATHMathSciNetGoogle Scholar
  4. [4]
    B. Korte and D. Hausmann, “An analysis of the greedy heuristic for independence systems,”Annals of Discrete Mathematics 2 (1978) 65–74.zbMATHMathSciNetCrossRefGoogle Scholar
  5. [5]
    B. Korte and L. Lovàsz, “Greedoids, a structural framework for the greedy algorithm,” in “Progress in Combinatorial Optimization” in: W.R. Pulleyblank, ed., Proceedings of the Silver Jubilee Conference on Combinatorics, Waterloo, June 1982, (Academic Press, London/New York/San Francisco, 1984) pp. 221–243.Google Scholar
  6. [6]
    A. Kotzig, “Eulerian lines in finite 4-valent graphs and their transformations,” in: Erdòs and Katona, eds,Theory of Graphs., Proceedings of the Colloquium held at Tihany (Hungary), Sept. 1966 (North-Holland, Amsterdam, 1968) pp. 219–230.Google Scholar
  7. [7]
    A. Schultze, personal communication, Oct. 1985.Google Scholar
  8. [8]
    E. Tardòs, “Generalized matroids,” to appear.Google Scholar
  9. [9]
    D.J.A. Welsh,Matroid Theory (Academic Press, London, 1976).zbMATHGoogle Scholar

Copyright information

© The Mathematical Programming Society, Inc 1987

Authors and Affiliations

  • André Bouchet
    • 1
  1. 1.Centre de Recherche en Informatique et CombinatoireUniversité du MaineLe MansFrance

Personalised recommendations