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On the Relative Complexity of 15 Problems Related to 0/1-Integer Programming

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Research Trends in Combinatorial Optimization

Summary

An integral part of combinatorial optimization and computational complexity consists of establishing relationships between different problems or different versions of the same problem. In this chapter, we bring together known and new, previously published and unpublished results, which establish that 15 problems related to optimizing a linear function over a 0/1-polytope are polynomial-time equivalent. This list of problems includes optimization and augmentation, testing optimality and primal separation, sensitivity analysis and inverse optimization, as well as several others.

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Author information

Authors and Affiliations

  1. Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA, 02139, USA

    Andreas S. Schulz

Authors
  1. Andreas S. Schulz
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Editor information

Editors and Affiliations

  1. Industrial and Systems Engineering, Georgia Tech, 765 Ferst Drive, Atlanta, Georgia, 30332-0205, USA

    William Cook

  2. Institute of Mathematics, Eötvös Loránd University, Pázmány Péter sétány 1/C, H-1117, Budapest, Hungary

    László Lovász

  3. Research Institute for Discrete Mathematics, University of Bonn, Lennéstr. 2, 53113, Bonn, Germany

    Jens Vygen

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Schulz, A.S. (2009). On the Relative Complexity of 15 Problems Related to 0/1-Integer Programming. In: Cook, W., Lovász, L., Vygen, J. (eds) Research Trends in Combinatorial Optimization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76796-1_19

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