Computational geometry: an introduction
Computational geometry: an introduction
Systolic algorithms to examine all pairs of elements
Communications of the ACM
Sorting numbers using limited systolic coprocessors
Information Processing Letters
Optimal simulations between mesh-connected arrays of processors
Journal of the ACM (JACM)
Sorting with efficient use of special-purpose sorters
Information Processing Letters
The input/output complexity of sorting and related problems
Communications of the ACM
Multidimensional divide-and-conquer
Communications of the ACM
Introduction to VLSI Systems
Efficient parallel techniques for computational geometry
Efficient parallel techniques for computational geometry
Scalable parallel geometric algorithms for coarse grained multicomputers
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
A randomized parallel 3D convex hull algorithm for coarse grained multicomputers
Proceedings of the seventh annual ACM symposium on Parallel algorithms and architectures
A Randomized Parallel Three-Dimensional Convex Hull Algorithm for Coarse-Grained Multicomputers
Theory of Computing Systems
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There is a large and growing body of literature concerning the solution of geometric problems on mesh-connected arrays of processors [5,9,14,17]. Most of these algorithms are optimal (i.e., run in time &Ogr;(n1/d) on a d-dimensional n-processor array), and they all assume that the parallel machine is trying to solve a problem of size n on an n-processor array. What happens when we have parallel machine for efficiently solving a problem of size p, and we are interested in using it to solve a problem of size n p? The answer to that question has to do with a fundamental, and yet (at least so far) little-studied property of geometric problems: their parallel-decomposability. More specifically, given that a problem of size p can be solved on a parallel machine P faster by a factor of (say) s(p) than on a RAM alone, then that problem is fully parallel-decomposable for P if a RAM to which the parallel machine P is attached can solve arbitrarily large problems with a speedup of also s(p) when compared to a RAM alone. The issue has been settled for the sorting problem when P is a linear systolic array [1,2,3,11]. Here we show that many geometric problems are fully parallel-decomposable for (multidimensional) mesh-connected arrays of processors.