The mean-partition problem

Abstract

In mean-partition problems the goal is to partition a finite set of elements, each associated with a d-vector, into p disjoint parts so as to optimize an objective, which depends on the averages of the vectors that are assigned to each of the parts. Each partition is then associated with a d x p matrix whose columns are the corresponding averages and a useful approach in studying the problem is to explore the mean-partition polytope, defined as the convex hull of the set of matrices associated with feasible partitions.