Journal of Parallel and Distributed Computing - Special issue: algorithms for hypercube computers
A bridging model for parallel computation
Communications of the ACM
Range search in parallel using distributed data structures
Journal of Parallel and Distributed Computing
Scalable parallel geometric algorithms for coarse grained multicomputers
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Multisearch techniques: parallel data structures on mesh-connected computers
Journal of Parallel and Distributed Computing
Communication-efficient parallel sorting (preliminary version)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Parallel Algorithms for Grounded Range Search and Applications
Euro-Par '99 Proceedings of the 5th International Euro-Par Conference on Parallel Processing
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The range tree is a fundamental data structure for multidimensional point sets, and as such, is central in a wide range of geometric and database applications. The authors 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, they show how to construct on a coarse grained multicomputer a distributed range tree T in time O(s/p+T/sub c/(s,p)), where s=n log/sup d-1/ n is the size of the sequential data structure and T,(s, p) is the time to perform an h-relations with h=/spl Theta/(s/p). They then show how T can be used to answer a given set Q of m=O(n) range queries in time O(s log n/p+T/sub c/(s,p)) and O(s log n/p+T/sub c/(s,p)+k/p), for the associative-function and 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 number of processors, plus a constant number of parallel communication rounds.