THE EQUIPARTITION POLYTOPE .1. FORMULATIONS, DIMENSION AND BASIC FACETS

The following basic clustering problem arises in different domains, ranging from physics, statistics and Boolean function minimization. Given a graph G = (V, E) and edge weights ce, partition the set V 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. An equicut is a feasible solution of the above problem and the equicut polytope Q(G) is the convex hull of the incidence vectors of equicuts in G. 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 for Q(G). © 1990 The Mathematical Programming Society, Inc.