Dynamic compressed hyperoctrees with application to the N-body problem

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 oft he points. Clarkson rectified the distributiondependency 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 ofdi mensions. © Springer-Verlag Berlin Heidelberg 1999.