Optimal Parallel All-Nearest-Neighbors Using the Well-Separated Pair Decomposition (1993)
| Venue: | In Proc. 34th IEEE Symposium on Foundations of Computer Science |
| Citations: | 25 - 1 self |
BibTeX
@INPROCEEDINGS{Callahan93optimalparallel,
author = {Paul B. Callahan},
title = {Optimal Parallel All-Nearest-Neighbors Using the Well-Separated Pair Decomposition},
booktitle = {In Proc. 34th IEEE Symposium on Foundations of Computer Science},
year = {1993},
pages = {332--340}
}
Years of Citing Articles
Bookmark
 |
 |
 |
 |
 |
 |
OpenURL
Abstract
We present an optimal parallel algorithm to construct the well-separated pair decomposition of a point set P in ! d . We show how this leads to a deterministic optimal O(logn) 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. 1 Introduction In [4] we introduced the well-separated pair decomposition of a set P of n points in ! d , and showed how to apply this decomposition to develop efficient parallel algorithms for two problems posed on multidimensional point sets. One of these applications led to the fastest known deterministic parallel algorithm for finding the k-nearest-neighbors of each point in P using O(n) processors. The time required for this algorithm is \Theta(log 2 n), which is within a log n factor of optimal. In this paper, we close the gap by developing an optimal O(log n) ti...
