Dynamic Compressed Hypertoctrees with Application to the N-Body Problem

Authors:
Srinivas Aluru;Fatih E. Sevilgen
Affiliations:
-;-
Venue:
Proceedings of the 19th Conference on Foundations of Software Technology and Theoretical Computer Science
Year:
1999

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Abstract

Hyperoctree is a popular data structure for organizing multidimensional point data. The main drawback ofthi s data structure is that its size and the run-time ofo perations supported by it are dependent upon the distribution of the points. Clarkson rectified the distribution-dependency in the size ofh yperoctrees by introducing compressed hyperoctrees. He presents an O(n log n) expected time randomized algorithm to construct a compressed hyperoctree. In this paper, we give three deterministic algorithms to construct a compressed hyperoctree in O(n log n) time, for any fixed dimension d. We present O(log n) algorithms for point and cubic region searches, point insertions and deletions. We propose a solution to the N-body problem in O(n) time, given the tree. Our algorithms also reduce the run-time dependency on the number of dimensions.