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An alternative approach for proving the NP-hardness of optimization problems

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  • Cheng, T.C.E.
  • Shafransky, Y.
  • Ng, C.T.

Abstract

We provide a new reduction-based approach for proving the NP-hardness of optimization problems and establish that it includes the “classical” approach as a special case. We apply our alternative approach to prove the NP-hardness of a problem for which the classical approach is not applicable. Besides, we construct a special case of the problem with the property that finding an optimal element takes polynomial time despite that computing the objective function values is NP-hard.

Suggested Citation

  • Cheng, T.C.E. & Shafransky, Y. & Ng, C.T., 2016. "An alternative approach for proving the NP-hardness of optimization problems," European Journal of Operational Research, Elsevier, vol. 248(1), pages 52-58.
    • Handle: RePEc:eee:ejores:v:248:y:2016:i:1:p:52-58
    DOI: 10.1016/j.ejor.2015.06.076
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    2. Yakov Shafransky & Viktor Shinkarevich, 2020. "On the complexity of constructing a minmax regret solution for the two-machine flow shop problem under the interval uncertainty," Journal of Scheduling, Springer, vol. 23(6), pages 745-749, December.

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