Integer Programming: Optimization and Evaluation Are Equivalent

  • James B. Orlin
  • Abraham P. Punnen
  • Andreas S. Schulz
Conference paper

DOI: 10.1007/978-3-642-03367-4_45

Part of the Lecture Notes in Computer Science book series (LNCS, volume 5664)
Cite this paper as:
Orlin J.B., Punnen A.P., Schulz A.S. (2009) Integer Programming: Optimization and Evaluation Are Equivalent. In: Dehne F., Gavrilova M., Sack JR., Tóth C.D. (eds) Algorithms and Data Structures. WADS 2009. Lecture Notes in Computer Science, vol 5664. Springer, Berlin, Heidelberg

Abstract

We show that if one can find the optimal value of an integer linear programming problem in polynomial time, then one can find an optimal solution in polynomial time. We also present a proper generalization to (general) integer programs and to local search problems of the well-known result that optimization and augmentation are equivalent for 0/1-integer programs. Among other things, our results imply that PLS-complete problems cannot have “near-exact” neighborhoods, unless PLS = P.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • James B. Orlin
    • 1
  • Abraham P. Punnen
    • 2
  • Andreas S. Schulz
    • 1
  1. 1.Massachusetts Institute of TechnologyCambridgeUSA
  2. 2.Simon Fraser UniversitySurreyCanada

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