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The Common Face of some 0/1-Polytopes with NP-Complete Nonadjacency Relation

Abstract

In this paper, we consider so-called double covering polytopes. In 1995, Matsui showed that the problem of checking nonadjacency on these polytopes is NP-complete. We show that double covering polytopes are faces of the following polytopes: knapsack polytopes, set covering polytopes, cubic subgraph polytopes, 3-SAT polytopes, partial order polytopes, traveling salesman polytopes, and some others.

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Correspondence to A. Maksimenko.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 18, No. 2, pp. 105–118, 2013.

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Maksimenko, A. The Common Face of some 0/1-Polytopes with NP-Complete Nonadjacency Relation. J Math Sci 203, 823–832 (2014). https://doi.org/10.1007/s10958-014-2172-9

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Keywords

  • Characteristic Vector
  • Convex Hull
  • Partial Order
  • Travel Salesman Problem
  • Knapsack Problem