Computational geometry: an introduction
Computational geometry: an introduction
Efficient parallel solutions to some geometric problems
Journal of Parallel and Distributed Computing
Mesh Computer Algorithms for Computational Geometry
IEEE Transactions on Computers
Parallel algorithms for regular architectures: meshes and pyramids
Parallel algorithms for regular architectures: meshes and pyramids
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
On the Average Number of Maxima in a Set of Vectors and Applications
Journal of the ACM (JACM)
Parallel permutation and sorting algorithms and a new generalized connection network
Journal of the ACM (JACM)
Multidimensional divide-and-conquer
Communications of the ACM
Determining the minimum-area encasing rectangle for an arbitrary closed curve
Communications of the ACM
What have we learnt from using real parallel machines to solve real problems?
C3P Proceedings of the third conference on Hypercube concurrent computers and applications - Volume 2
Dynamic computational geometry on parallel computers
C3P Proceedings of the third conference on Hypercube concurrent computers and applications - Volume 2
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This paper gives hypercube algorithms for some simple problems involving geometric properties of sets of points. The properties considered emphasize aspects of convexity and domination. Efficient algorithms are given for both fine-grain and medium-grain hypercube computers. For both serial and parallel computers, sorting plays an important role in geometric algorithms for determining simple properties, often being the dominant component of the time. On a hypercube computer the time required to sort is still not fully understood, so the times of some of our algorithms for unsorted data are not completely determined. For the fine-grain model using worst case timing we show that if the data is presorted then faster algorithms are possible, if sorting one item per processor requires time growing faster than the dimension of the hypercube. For both models we show that faster algorithms are possible for point sets generated randomly, when time is measured using expected time. Our algorithms are developed for sets of planar points, with several of them extending to sets of points in spaces of higher dimension.