article

Constructing arrangements optimally in parallel

Author:

Michael T. GoodrichAuthors Info & Claims

Discrete & Computational Geometry, Volume 9, Issue 4

Pages 371 - 385

https://doi.org/10.1007/BF02189329

Published: 01 December 1993 Publication History

Abstract

We give two optimal parallel algorithms for constructing the arrangement ofn lines in the plane. The first nethod is quite simple and runs inO(log2n) time usingO(n2) work, and the second method, which is more sophisticated, runs inO(logn) time usingO(n2) work. This second result solves a well-known open problem in parallel computational geometry, and involves the use of a new algorithmic technique, the construction of an -pseudocutting. Our results immediately imply that the arrangement ofn hyperplanes in d inO(logn) time usingO(nd) work, for fixedd, can be optimally constructed. Our algorithms are for the CREW PRAM.

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Cited By

Aghamolaei SKeikha VGhodsi MMohades A(2021)Windowing queries using Minkowski sum and their extension to MapReduceThe Journal of Supercomputing10.1007/s11227-020-03299-777:1(936-972)Online publication date: 1-Jan-2021
https://dl.acm.org/doi/10.1007/s11227-020-03299-7
Dévai F(2011)An optimal hidden-surface algorithm and its parallelizationProceedings of the 2011 international conference on Computational science and its applications - Volume Part III10.5555/2029312.2029314(17-29)Online publication date: 20-Jun-2011
https://dl.acm.org/doi/10.5555/2029312.2029314
Chazelle BLeighton FGoodrich M(1994)Computational geometryProceedings of the twenty-sixth annual ACM symposium on Theory of Computing10.1145/195058.195110(75-94)Online publication date: 23-May-1994
https://dl.acm.org/doi/10.1145/195058.195110

Constructing arrangements optimally in parallel
1. Computing methodologies
  1. Computer graphics
  2. Parallel computing methodologies
2. Theory of computation

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Published In

cover image Discrete & Computational Geometry

Discrete & Computational Geometry Volume 9, Issue 4

April 1993

92 pages

ISSN:0179-5376

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Copyright © Copyright © 1993 Springer-Verlag New York Inc.

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 December 1993

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Cited By

Aghamolaei SKeikha VGhodsi MMohades A(2021)Windowing queries using Minkowski sum and their extension to MapReduceThe Journal of Supercomputing10.1007/s11227-020-03299-777:1(936-972)Online publication date: 1-Jan-2021
https://dl.acm.org/doi/10.1007/s11227-020-03299-7
Dévai F(2011)An optimal hidden-surface algorithm and its parallelizationProceedings of the 2011 international conference on Computational science and its applications - Volume Part III10.5555/2029312.2029314(17-29)Online publication date: 20-Jun-2011
https://dl.acm.org/doi/10.5555/2029312.2029314
Chazelle BLeighton FGoodrich M(1994)Computational geometryProceedings of the twenty-sixth annual ACM symposium on Theory of Computing10.1145/195058.195110(75-94)Online publication date: 23-May-1994
https://dl.acm.org/doi/10.1145/195058.195110

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