Derivations of Clustering Performance of Spatial Access Methods

This paper develops analytical expressions and algorithms for deriving the number of clusters that an average query of a given size and orientation retrieves using a given spatial access method. Besides being of theoretical interest, these algorithms run very fast and can be used by query schedulers and optimizers on the fly to determine best processing plans. Current techniques for determining the number of clusters are based on simulation, which is slow. Our algorithms are discussed in the context of the hilbert method for ease of exposition, but they do generalize in most cases to other space filling methods. Moreover, they apply for any given blocking factor. We prove that the proposed approach provides exact results for the case of blocking factor of 1, and empirically demonstrate that it yields near exact results for other blocking factors.