Computational geometry: an introduction
Computational geometry: an introduction
SIAM Journal on Computing
Parallel construction of subdivision hierarchies
Journal of Computer and System Sciences
An optimal parallel algorithm for building a data structure for planar point location
Journal of Parallel and Distributed Computing
Determining the separation of preprocessed polyhedra: a unified approach
Proceedings of the seventeenth international colloquium on Automata, languages and programming
Parallel algorithms for shared-memory machines
Handbook of theoretical computer science (vol. A)
Convex hulls of finite sets of points in two and three dimensions
Communications of the ACM
New Parallel Algorithms for Convex Hull and Triangulation in 3-Dimensional Space
MFCS '92 Proceedings of the 17th International Symposium on Mathematical Foundations of Computer Science
Parallel algorithms for geometric problems
Parallel algorithms for geometric problems
SCG '94 Proceedings of the tenth 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 Simple Voronoi Diagram Algorithm for a Reconfigurable Mesh
IEEE Transactions on Parallel and Distributed Systems
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
gHull: A GPU algorithm for 3D convex hull
ACM Transactions on Mathematical Software (TOMS)
A Randomized Parallel Three-Dimensional Convex Hull Algorithm for Coarse-Grained Multicomputers
Theory of Computing Systems
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In this paper we present an Ologn time parallel algorithm for computing the convex hullof n points in R3. This algorithm uses On1+a processors on a CREW PRAM, for any constant 0 Olog2n. In addition, the algorithm presented here is thefirst parallel algorithm for the three-dimensional convex hull problemthat is not based on the serial divide-and-conquer algorithm ofPreparata and Hong, whose crucial operation is the merging of the convexhulls of two linearly separated point sets. The contributions of thispaper are therefore (i) an Ologn time parallel algorithm for the three-dimensionalconvex hull problem, and (ii) a parallel algorithm for this problemthat does not follow the traditional divide-and-conquer paradigm.