Skip to main content
Log in

On submodular function minimization

  • Published:
Combinatorica Aims and scope Submit manuscript

Abstract

Earlier work of Bixby, Cunningham, and Topkis is extended to give a combinatorial algorithm for the problem of minimizing a submodular function, for which the amount of work is bounded by a polynomial in the size of the underlying set and the largest function value (not its length).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. R. E. Bixby, W. H. Cunningham andD. M. Topkis, The poset of a polymatroid extreme point,Math. of Operations Res., to appear.

  2. A. Bouchet,private communication, 1984.

  3. W. H. Cunningham, Decomposition of directed graphs,SIAM J. Alg. and Disc. Methods 3 (1982), 214–228.

    Article  MATH  MathSciNet  Google Scholar 

  4. W. H. Cunningham, Decomposition of submodular functions,Combinatorica 3 (1983), 53–68.

    MATH  MathSciNet  Google Scholar 

  5. W. H. Cunningham, Testing membership in matroid polyhedra,Journal of Combinatorial Theory (B) 36 (1984), 161–188.

    Article  MATH  MathSciNet  Google Scholar 

  6. W. H. Cunningham, Minimum cuts, modular functions, and matroid polyhedra,Networks, to appear.

  7. J. Edmonds, Submodular functions, matroids, and certain polyhedra, in:Combinatorial Structures and their Applications (ed.: R. K. Guy et al.), Gordon and Breach, New York, 1970.

    Google Scholar 

  8. M. Grötschel, L. Lovász andA. Schrijver, The ellipsoid method and its consequences in combinatorial optimization,Combinatorica 1 (1981), 169–197.

    MATH  MathSciNet  Google Scholar 

  9. L. Lovász, Submodular functions and convexity, in:Mathematical Programming: The State of the Art (ed: A. Bachem et al.), Springer-Verlag (1983), 235–257.

Download references

Author information

Authors and Affiliations

Authors

Additional information

Research partially supported by a grant from the Natural Sciences and Engineering Research Council of Canada.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cunningham, W.H. On submodular function minimization. Combinatorica 5, 185–192 (1985). https://doi.org/10.1007/BF02579361

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02579361

AMS subject classification (1980)

Navigation