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Integer Programming: Optimization and Evaluation Are Equivalent

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Algorithms and Data Structures (WADS 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5664))

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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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Author information

Authors and Affiliations

  1. Massachusetts Institute of Technology, Cambridge, MA, USA

    James B. Orlin & Andreas S. Schulz

  2. Simon Fraser University, Surrey, BC, Canada

    Abraham P. Punnen

Authors
  1. James B. Orlin
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  2. Abraham P. Punnen
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  3. Andreas S. Schulz
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Editor information

Editors and Affiliations

  1. Carleton University, Ottawa, Canada

    Frank Dehne

  2. Department of Computer Science, University of Calgary, 2500 University Drive N.W., T2N 1N4, Calgary, AB, Canada

    Marina Gavrilova

  3. School of Computer Science, Carleton University, 1125 Colonel By Drive, Ottawa, P.O. Box, K1S 5B6, Ontario, Canada

    Jörg-Rüdiger Sack

  4. University of Calgary, Calgary, AB, Canada

    Csaba D. Tóth

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© 2009 Springer-Verlag Berlin Heidelberg

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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. https://doi.org/10.1007/978-3-642-03367-4_45

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  • DOI: https://doi.org/10.1007/978-3-642-03367-4_45

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03366-7

  • Online ISBN: 978-3-642-03367-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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