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IASI Research Report n. 195 (Previous Next) Conforti M.,

Rao M.R.,

Sassano A.The equipartition polytope I: formulations, dimension and basic facets.ABSTRACT The following basic clustering problem arises in different domains, ranging from phisics, statistics and Boolean function minimization.
Given a graph G = (V, E) and edge weights c_e, partition the set V into two sets of ... and ... 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).