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 Diskr. Mat., 2017, Volume 29, Issue 2, Pages 29–39 (Mi dm1427)

On a family of 0/1-polytopes with an NP-complete criterion for vertex nonadjacency relation

A. N. Maksimenko

P.G. Demidov Yaroslavl State University

Abstract: In 1995 T. Matsui considered a special family of 0/1-polytopes with an NP-complete criterion for vertex nonadjacency relation. In 2012 the author demonstrated that all polytopes of this family appear as faces of polytopes associated with the following NP-complete problems: the travelling salesman problem, the 3-satisfiability problem, the knapsack problem, the set covering problem, the partial ordering problem, the cube subgraph problem, and some others. Here it is shown that none of the polytopes of the aforementioned special family (with the exception of the one-dimensional segment) can appear as a face in a polytope associated with the problem of the maximum independent set, the set packing problem, the set partitioning problem, and the problem of 3-assignments.

Keywords: affine reduction, set covering, set partitioning.

 Funding Agency Grant Number Russian Academy of Sciences - Federal Agency for Scientific Organizations 1.5768.2017/Ï220

DOI: https://doi.org/10.4213/dm1427

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English version:
Discrete Mathematics and Applications, 2019, 29:1, 7–14

Bibliographic databases:

UDC: 519.854.2

Citation: A. N. Maksimenko, “On a family of 0/1-polytopes with an NP-complete criterion for vertex nonadjacency relation”, Diskr. Mat., 29:2 (2017), 29–39; Discrete Math. Appl., 29:1 (2019), 7–14

Citation in format AMSBIB
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