Explicit solution of partitioning problems over a 1-dimensional parameter space

Abstract

We consider a class of partitioning problems where the partitioned set is a finite set of real numbers and the objective function of a partition is a function of the vector whose coordinates are the sums of the elements in each part of the given partition (the number of such parts is assumed given). We obtain an explicit solution of such partitioning problem with polynomial complexity bounds. (C) 2000 John Wiley & Sons, Inc.