Algorithms and Data Structures

Volume 5664 of the series Lecture Notes in Computer Science pp 519-529

Integer Programming: Optimization and Evaluation Are Equivalent

  • James B. OrlinAffiliated withMassachusetts Institute of Technology
  • , Abraham P. PunnenAffiliated withSimon Fraser University
  • , Andreas S. SchulzAffiliated withMassachusetts Institute of Technology

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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.