This article is cited 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 $U=\{u_1,u_2,\dots,u_d\}$ 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.

UDC: 519.85

Received: 19.07.2010
Revised: 15.03.2011

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