Randomized parallel algorithms for trapezoidal diagrams

Kenneth L. Clarkson, Richard Cole, Robert E. Tarjan

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We describe randomized parallel CREW PRAM algorithms for building trapezoidal diagrams of line segments in the plane. For general segments, we give an algorithm requiring optimal O(A + nlogn) expected work and optimal O(logn) time, where A is the number of intersecting pairs of segments. If the segments form a simple chain, we give an algorithm requiring optimal O(n) expected work and O(log n log log ra log n) expected time, and a simpler algorithm requiring O(n log n) expected work. The serial algorithm corresponding to the latter is the simplest known algorithm requiring O(n log n) expected operations. For a set of segments forming K chains, we give an algorithm requiring O(A + n log n + K log n) expected work and O(log n log log n log n) expected time. The parallel time bounds require the assumption that enough processors are available, with processor allocations every log n steps.

Original languageEnglish (US)
Title of host publicationProceedings of the Annual Symposium on Computational Geometry
PublisherAssociation for Computing Machinery
Pages152-161
Number of pages10
VolumePart F129851
ISBN (Print)0897914260
DOIs
StatePublished - Jun 1 1991
Event7th Annual Symposium on Computational Geometry, SCG 1991 - North Conway, United States
Duration: Jun 10 1991Jun 12 1991

Other

Other7th Annual Symposium on Computational Geometry, SCG 1991
CountryUnited States
CityNorth Conway
Period6/10/916/12/91

Fingerprint

Randomized Algorithms
Parallel algorithms
Parallel Algorithms
Diagram
Optimal Algorithm
Line segment

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Computational Mathematics

Cite this

Clarkson, K. L., Cole, R., & Tarjan, R. E. (1991). Randomized parallel algorithms for trapezoidal diagrams. In Proceedings of the Annual Symposium on Computational Geometry (Vol. Part F129851, pp. 152-161). Association for Computing Machinery. https://doi.org/10.1145/109648.109665

Randomized parallel algorithms for trapezoidal diagrams. / Clarkson, Kenneth L.; Cole, Richard; Tarjan, Robert E.

Proceedings of the Annual Symposium on Computational Geometry. Vol. Part F129851 Association for Computing Machinery, 1991. p. 152-161.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Clarkson, KL, Cole, R & Tarjan, RE 1991, Randomized parallel algorithms for trapezoidal diagrams. in Proceedings of the Annual Symposium on Computational Geometry. vol. Part F129851, Association for Computing Machinery, pp. 152-161, 7th Annual Symposium on Computational Geometry, SCG 1991, North Conway, United States, 6/10/91. https://doi.org/10.1145/109648.109665
Clarkson KL, Cole R, Tarjan RE. Randomized parallel algorithms for trapezoidal diagrams. In Proceedings of the Annual Symposium on Computational Geometry. Vol. Part F129851. Association for Computing Machinery. 1991. p. 152-161 https://doi.org/10.1145/109648.109665
Clarkson, Kenneth L. ; Cole, Richard ; Tarjan, Robert E. / Randomized parallel algorithms for trapezoidal diagrams. Proceedings of the Annual Symposium on Computational Geometry. Vol. Part F129851 Association for Computing Machinery, 1991. pp. 152-161
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