d-Dimensional Range Search on Multicomputers

The range tree is a fundamental data structure for multidimensional point sets, and as such, is central in a wide range of geometric anddatabaseapplications. Inthis paper, we describe the first non-trivial adaptation of range trees to the parallel distributed memory setting (BSP like models). Given a set L of n points in d-dimensional Cartesian space, we show how to construct on a coarse grained multicomputer a distributed range tree T in time Os p + Tcs;p, where s = nlogd,1 n is the size of the sequential data structure and Tcs;p is the time to perform an h-relations with h = s=p. We then show how T can be used to answer a given set Q of m = On range queries in time O(slog n p + Tcs;p) and O(slog n p + Tcs;p + k p), for the associative-functionand report modes respectively, where k is the number of results to be reported. These parallel construction and search algorithms are both highly efficient, in that their running times are the sequential time divided by the num...

• Type: Conference
• Year: 1997
• Where: IPPS
• Authors: Afonso Ferreira, Claire Kenyon, Andrew Rau-Chaplin, Stéphane Ubéda
• Keywords: Data Structure, Distributed And Parallel Computing, IPPS 1997, Range Tree, first Non-trivial Adaptation