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4OR

, Volume 11, Issue 3, pp 249–252 | Cite as

Complexity and in-approximability of a selection problem in robust optimization

  • Vladimir G. Deineko
  • Gerhard J. Woeginger
Research paper

Abstract

We establish strong NP-hardness and in-approximability of the so-called representatives selection problem, a tool selection problem in the area of robust optimization. Our results answer a recent question of Dolgui and Kovalev (4OR Q J Oper Res 10:181–192, 2012).

Keywords

Combinatorial optimization Computational complexity  Robust optimization 

Mathematics Subject Classification

03D15 62F35 

Notes

Acknowledgments

Vladimir Deineko acknowledges support by Warwick University’s Centre for Discrete Mathematics and Its Applications (DIMAP) and by EPSRC fund EP/F017871. Gerhard Woeginger acknowledges support by the Netherlands Organization for Scientific Research (NWO), grant 639.033.403, and by DIAMANT (an NWO mathematics cluster).

References

  1. Aissi H, Bazgan C, Vanderpooten D (2009) Minmax and minmax regret versions of combinatorial optimization problems: a survey. Eur J Oper Res 197:427–438Google Scholar
  2. Dolgui A, Kovalev S (2012) Min-max and min-max (relative) regret approaches to representatives selection problem. 4OR Q J Oper Res 10:181–192CrossRefGoogle Scholar
  3. Garey MR, Johnson DS (1979) Computers and intractability: a guide to the theory of NP-completeness. Freeman, San FranciscoGoogle Scholar
  4. Khot S, Regev O (2008) Vertex cover might be hard to approximate to within \(2-\varepsilon \). J Comput Syst Sci 74:335–349CrossRefGoogle Scholar
  5. Kouvelis P, Yu G (1997) Robust discrete optimization and its applications. Kluwer Academic Publishers, BostonCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Warwick Business SchoolThe University of WarwickCoventryUK
  2. 2.Department of Mathematics and Computer ScienceTU EindhovenEindhovenThe Netherlands

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