Probabilistic analysis of some euclidean clustering problems

We are given n points distributed randomly in a compact region D of R^m. We consider various optimisation problems associated with partitioning this set of points into k subsets. For each problem we demonstrate lower bounds which are satisfied with high probability. For the case where D is a hypercube we use a partitioning technique to give deterministic upper bounds and to construct algorithms which with high probability can be made arbitrarily accurate in polynomial time for a given required accuracy.