Skip to main content
SpringerLink
Log in

Complexity of some parametric integer and network programming problems

  • Published:
Mathematical Programming Submit manuscript

Abstract

Two examples of parametric cost programming problems—one in network programming and one in NP-hard 0-1 programming—are given; in each case, the number of breakpoints in the optimal cost curve is exponential in the square root of the number of variables in the problem.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. D. Gusfield, “Sensitivity analysis for combinatorial optimization”, Memorandum number UCB/ERL M80/22, Electronics Research Laboratory (Berkeley, CA, 1980).

    Google Scholar 

  2. O.H. Ibarra and C.E. Kim, “Fast approximation algorithms for the knapsack and sum of subset problem”,Journal of the Association for Computing Machinery 22 (1975) 463–468.

    MATH  MathSciNet  Google Scholar 

  3. V. Klee and G.J. Minty, “How good is the simplex algorithm?”, in O. Shisha, Ed.,Inequalities III (Academic Press, New York, 1969) pp. 159–175.

    Google Scholar 

  4. G. Mathews, “On the partition of numbers”,Proceedings of the London Mathematical Society 28 (1897) 486–490.

    Article  Google Scholar 

  5. K. Murty, “Computational complexity of parametric linear programming”,Mathematical Programming 19 (1980) 213–219.

    Article  MATH  MathSciNet  Google Scholar 

  6. R. Rockafellar,Convex analysis (Princeton University Press, Princeton, NJ, 1970).

    MATH  Google Scholar 

  7. I.G. Rosenberg, “Aggregation of equations in integer programming,“Discrete Mathematics 10 (1974) 325–341.

    Article  MATH  MathSciNet  Google Scholar 

  8. H. Stone, “Multiprocessor scheduling with aid ne.work flow algorithms”,IEEE Transactions on Software Engineering SE-3 (1977) 85–93.

    Google Scholar 

  9. H. Stone, “Critical load factors”,IEEE Transactions on Software Engineering SE-4 (1978) 254–258.

    Google Scholar 

  10. N. Zadeh, “A bad network problem for the simplex method and other minimum cost flow algorithms”,Mathematical Programming 5 (1973) 255–266.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Michigan, Ann Arbor, MI, USA

    Patricia J. Carstensen

Authors
  1. Patricia J. Carstensen
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This research is partially supported by the Air Force Office of Scientic Research. Air Force Number AFOSR-78-3646

Rights and permissions

Reprints and permissions

About this article

Cite this article

Carstensen, P.J. Complexity of some parametric integer and network programming problems. Mathematical Programming 26, 64–75 (1983). https://doi.org/10.1007/BF02591893

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02591893

Key words

Search

Navigation