Efficient Parallel Convex Hull Algorithms
IEEE Transactions on Computers
A bridging model for parallel computation
Communications of the ACM
How to net a lot with little: small &egr;-nets for disks and halfspaces
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Optimal parallel randomized algorithms for three-dimensional convex hulls and related problems
SIAM Journal on Computing
Parallel sorting by regular sampling
Journal of Parallel and Distributed Computing
Reporting points in halfspaces
Computational Geometry: Theory and Applications
Parallel computing (2nd ed.): theory and practice
Parallel computing (2nd ed.): theory and practice
Approximations and optimal geometric divide-and-conquer
Selected papers of the 23rd annual ACM symposium on Theory of computing
The bulk-synchronous parallel random access machine
Theoretical Computer Science - Special issue on parallel computing
Handbook of discrete and computational geometry
Handbook of discrete and computational geometry
Handbook of discrete and computational geometry
Handbook of discrete and computational geometry
Parallel algorithms in geometry
Handbook of discrete and computational geometry
Scalable 2D convex hull and triangulation algorithms for coarse grained multicomputers
Journal of Parallel and Distributed Computing
Randomized fully-scalable BSP techniques for multi-searching and convex hull construction
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
A 2-D parallel convex hull algorithm with optimal communication phases
Parallel Computing
Euro-Par '96 Proceedings of the Second International Euro-Par Conference on Parallel Processing - Volume I
Parallel algorithms for higher-dimensional convex hulls
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Parallel selection by regular sampling
Euro-Par'10 Proceedings of the 16th international Euro-Par conference on Parallel processing: Part II
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The model of bulk-synchronous parallel (BSP) computation is an emerging paradigm of general-purpose parallel computing. We propose the first optimal deterministic BSP algorithm for computing the convex hull of a set of points in three-dimensional Euclidean space. Our algorithm is based on known fundamental results from combinatorial geometry, concerning small-sized, efficiently constructible 驴-nets and 驴-approximations of a given point set. The algorithm generalises the technique of regular sampling, used previously for sorting and two-dimensional convex hull computation. The cost of the simple algorithm is optimal only for extremely large inputs; we show how to reduce the required input size by applying regular sampling in a multi-level fashion.