The equipartition polytope. I: Formulations, dimension and basic facets (original) (raw)

Mathematical Programming, 1990

Abstract

The following basic clustering problem arises in different domains, ranging from physics, statistics and Boolean function minimization. Given a graphG = (V, E) and edge weightsc e , partition the setV into two sets of ⌈1/2|V|⌉ and ⌊1/2|V|⌋ nodes in such a way that the sum of the weights of edges not having both endnodes in the same set is maximized or minimized. Anequicut is a feasible solution of the above problem and theequicut polytope Q(G) is the convex hull of the incidence vectors of equicuts inG. In this paper we give some integer programming formulations of the equicut problem, study the dimension of the equicut polytope and describe some basic classes of facet-inducing inequalities forQ(G).

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