منابع مشابه
Gap Inequalities for the Cut Polytope
We introduce a new class of inequalities valid for the cut polytope, which we call gap inequalities. Each gap inequality is given by a nite sequence of integers, whose \gap" is deened as the smallest discrepancy arising when decomposing the sequence into two parts as equal as possible. Gap inequalities include the hypermetric inequalities and the negative type inequalities, which have been exte...
متن کاملOn the Gap Inequalities for the Max-Cut Problem
Laurent & Poljak introduced a class of valid inequalities for the max-cut problem, called gap inequalities, which include many other known inequalities as special cases. The gap inequalities have received little attention and are poorly understood. This paper presents the first ever computational results. In particular, we start presenting a cuttingplane scheme based on an effective heuristic s...
متن کاملNew classes of facets of the cut polytope and tightness of Imm22 Bell inequalities
The Grishukhin inequality is a facet of the cut polytope CUT7 of the complete graph K7, for which no natural generalization to a family of inequalities has previously been found. On the other hand, the Imm22 Bell inequalities of quantum information theory, found by Collins and Gisin, can be seen as valid inequalities of the cut polytope CUT¤(K1,m,m) of the complete tripartite graph K1,m,m. They...
متن کاملOn the Graph Bisection Cut Polytope
Given a graph G = (V,E) with node weights φv ∈ N ∪ {0}, v ∈ V , and some number F ∈ N∪{0}, the convex hull of the incidence vectors of all cuts δ(S), S ⊆ V with φ(S) ≤ F and φ(V \ S) ≤ F is called the bisection cut polytope. We study the facial structure of this polytope which shows up in many graph partitioning problems with applications in VLSI-design or frequency assignment. We give necessar...
متن کاملOn the directed cut cone and polytope
In this paper we study the directed cut cone and polytope which are the positive hull and convex hull of all directed cut vectors of a complete directed graph, respectively. We present results on the polyhedral structure of these polyhedra. A relation between directed cut polyhedra and undirected cut polyhedra is established that provides families of facet defining inequalities for directed cut...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 1996
ISSN: 0195-6698
DOI: 10.1006/eujc.1996.0020