Proceedings of the twelfth annual symposium on Computational geometry
A Randomized Algorithm for Voronoi Diagram of Line Segments on Coarse-Grained Multiprocessors
IPPS '96 Proceedings of the 10th International Parallel Processing Symposium
A 2-D Parallel Convex Hull Algorithm with Optimal Communication Phases
IPPS '97 Proceedings of the 11th International Symposium on Parallel Processing
A Parallel Algorithm for Finding the Constrained Voronoi Diagram of Line Segments in the Plane
WADS '99 Proceedings of the 6th International Workshop on Algorithms and Data Structures
Parallel Convex Hull Computation by Generalised Regular Sampling
Euro-Par '02 Proceedings of the 8th International Euro-Par Conference on Parallel Processing
Improved Deterministic Parallel Padded Sorting
ESA '98 Proceedings of the 6th Annual European Symposium on Algorithms
Computing the Diameter of a Point Set
DGCI '02 Proceedings of the 10th International Conference on Discrete Geometry for Computer Imagery
Recursion and parallel algorithms in geometric modeling problems
Cybernetics and Systems Analysis
The system of common algorithmic space to create visual models of phenomena and processes
Proceedings of the International Conference on Applications of Computer and Information Sciences to Nature Research
ICA3PP'05 Proceedings of the 6th international conference on Algorithms and Architectures for Parallel Processing
Applications of Geometry Processing: CudaHull: Fast parallel 3D convex hull on the GPU
Computers and Graphics
A Randomized Parallel Three-Dimensional Convex Hull Algorithm for Coarse-Grained Multicomputers
Theory of Computing Systems
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We give fast randomized and deterministic parallel methods for constructing convex hulls in R/sup d/, for any fixed d. Our methods are for the weakest shared-memory model, the EREW PRAM, and have optimal work bounds (with high probability for the randomized methods). In particular, we show that the convex hull of n points in R/sup d/ can be constructed in O(log n) time using O(n log n+n/sup [d/2]/) work, with high probability. We also show that it can be constructed deterministically in O(log/sup 2/ n) time using O(n log n) work for d=3 and in O(log n) time using O(n/sup [d/2]/ log/sup c([d/2]-[d/2]/) n) work for d/spl ges/4, where c0 is a constant which is optimal for even d/spl ges/4. We also show how to make our 3-dimensional methods output-sensitive with only a small increase in running time. These methods can be applied to other problems as well.