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Diskretn. Anal. Issled. Oper., 2011, Volume 18, Number 3, Pages 76–83 (Mi da655)  

This article is cited in 4 scientific papers (total in 4 papers)

SAT polytopes are faces of polytopes of the traveling salesman problem

A. N. Maksimenko

P. G. Demidov Yaroslavl State University, Yaroslavl, Russia

Abstract: Let $U=\{u_1,u_2,…,u_d\}$ be a set of boolean variables and $C$ be a boolean formula over $U$ in conjunctive normal form. Denote by $Y$ the set of characteristic vectors of all satisfying truth assignments for $C$. The SAT polytope, denoted by $S(U,C)$, is the convex hull of $Y$. Denote by $T_n$ the asymmetric traveling salesman polytope. We show that $S(U,C)$ is a face of $T_n$, for $n=|U|+2\operatorname{len}(C)$, and $\operatorname{len}(C)$ is the size of the formula $C$. Ill. 1, Bibliogr. 9.

Keywords: TSP polytope, SAT polytope, face.

Full text: PDF file (264 kB)
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Bibliographic databases:
UDC: 519.85
Received: 19.07.2010
Revised: 15.03.2011

Citation: A. N. Maksimenko, “SAT polytopes are faces of polytopes of the traveling salesman problem”, Diskretn. Anal. Issled. Oper., 18:3 (2011), 76–83

Citation in format AMSBIB
\Bibitem{Mak11}
\by A.~N.~Maksimenko
\paper SAT polytopes are faces of polytopes of the traveling salesman problem
\jour Diskretn. Anal. Issled. Oper.
\yr 2011
\vol 18
\issue 3
\pages 76--83
\mathnet{http://mi.mathnet.ru/da655}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2883749}
\zmath{https://zbmath.org/?q=an:1249.90327}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. N. Maksimenko, “An analog of the Cook theorem for polytopes”, Russian Math. (Iz. VUZ), 56:8 (2012), 28–34  mathnet  crossref  mathscinet
    2. A. V. Seliverstov, “On monomials in quadratic forms”, J. Appl. Industr. Math., 7:3 (2013), 431–434  mathnet  crossref  mathscinet
    3. A. N. Maksimenko, “$k$-neighborly faces of the Boolean quadric polytopes”, J. Math. Sci., 203:6 (2014), 816–822  mathnet  crossref  mathscinet
    4. A. N. Maksimenko, “A special role of Boolean quadratic polytopes among other combinatorial polytopes”, Model. i analiz inform. sistem, 23:1 (2016), 23–40  mathnet  crossref  mathscinet  elib
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