Optimal parallel all-nearest-neighbors using the well-separated pair decomposition

Authors:
P. B. Callahan
Affiliations:
Dept. of Comput. Sci., Johns Hopkins Univ., Baltimore, MD, USA
Venue:
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
Year:
1993

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Abstract

We present an optimal parallel algorithm to construct the well-separated pair decomposition of a point set P in R/sup d/. We show how this leads to a deterministic optimal O(log n) time parallel algorithm for finding the k nearest neighbors of each point in P, where k is a constant. We discuss several additional applications of the well-separated pair decomposition for which we can derive faster parallel algorithms.