A logarithmic time sort for linear size networks
Journal of the ACM (JACM)
A probabilistic algorithm for the post office problem
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Parallel processing for efficient subdivision search
SCG '87 Proceedings of the third annual symposium on Computational geometry
Randomized algorithms and pseudorandom numbers
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Optimal and sublogarithmic time randomized parallel sorting algorithms
SIAM Journal on Computing
Applications of random sampling in computational geometry, II
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Algorithms for diametral pairs and convex hulls that are optimal, randomized, and incremental
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Optimal parallel algorithms for polygon and point-set problems
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Applications of random sampling in computational geometry, II
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
STOC '75 Proceedings of seventh annual ACM symposium on Theory of computing
Optimal Randomized Parallel Algorithms for Computational Geometry I
Optimal Randomized Parallel Algorithms for Computational Geometry I
Parallel algorithms for geometric problems
Parallel algorithms for geometric problems
Efficient parallel computation of arrangements of hyperplanes in d dimensions
SPAA '90 Proceedings of the second annual ACM symposium on Parallel algorithms and architectures
Parallel algorithms for arrangements
SPAA '90 Proceedings of the second annual ACM symposium on Parallel algorithms and architectures
Randomized algorithms for binary search and load balancing with geometric applications
SPAA '90 Proceedings of the second annual ACM symposium on Parallel algorithms and architectures
In-place techniques for parallel convex hull algorithms (preliminary version)
SPAA '91 Proceedings of the third annual ACM symposium on Parallel algorithms and architectures
Ultra-fast expected time parallel algorithms
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
An efficient expected time parallel algorithm for Voronoi construction
SPAA '92 Proceedings of the fourth annual ACM symposium on Parallel algorithms and architectures
On randomization in sequential and distributed algorithms
ACM Computing Surveys (CSUR)
Efficient NC algorithms for set cover with applications to learning and geometry
Proceedings of the 30th IEEE symposium on Foundations of computer science
Developing a practical projection-based parallel Delaunay algorithm
Proceedings of the twelfth annual symposium on Computational geometry
Implementation and evaluation of an efficient parallel Delaunay triangulation algorithm
Proceedings of the ninth annual ACM symposium on Parallel algorithms and architectures
A Simple Voronoi Diagram Algorithm for a Reconfigurable Mesh
IEEE Transactions on Parallel and Distributed Systems
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We introduce a new randomized sampling technique, called Polling which has applications to deriving efficient parallel algorithms. As an example of its use in computational geometry, we present an optimal parallel randomized algorithm for intersection of half-spaces in three dimensions. Because of well-known reductions, our methods also yield equally efficient algorithms for fundamental problems like the convex hull in three dimensions, Voronoi diagram of point sites on a plane and Euclidean minimal spanning tree. Our algorithms run in time T = O(logn) for worst-case inputs and uses P = O(n) processors in a CREW PRAM model where n is the input size. They are randomized in the sense that they use a total of only O(log2 n) random bits and terminate in the claimed time bound with probability 1 - n-&agr; for any &agr; 0. They are also optimal in P . T product since the sequential time bound for all these problems is &OHgr;(nlogn). The best known determistic parallel algorithms for 2-D Voronoi-diagram and 3-D Convex hull run in O(log2 n) and O(log2 nlog * n) time respectively while using O(n) processors.