Convex Clusters in a Discrete m-Dimensional Space

Abstract

A simple procedure is used to dynamically create convex clusters of items in a discrete m-dimensional space. Systems of difference equations are derived that describe the behavior of this cluster formation under the assumption that individual clusters are either of bounded or unbounded size. These equations are used to calculate the expected number and size of such clusters given the number n of items. For an actual implemented database access and retrieval method, these results provide a way of determining both the expected storage overhead and the expected retrieval costs.