### 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 language | English (US) |
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Title of host publication | Proceedings of the Annual Symposium on Computational Geometry |

Publisher | Association for Computing Machinery |

Pages | 152-161 |

Number of pages | 10 |

Volume | Part F129851 |

ISBN (Print) | 0897914260 |

DOIs | |

State | Published - Jun 1 1991 |

Event | 7th Annual Symposium on Computational Geometry, SCG 1991 - North Conway, United States Duration: Jun 10 1991 → Jun 12 1991 |

### Other

Other | 7th Annual Symposium on Computational Geometry, SCG 1991 |
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Country | United States |

City | North Conway |

Period | 6/10/91 → 6/12/91 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Geometry and Topology
- Computational Mathematics

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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

}

TY - GEN

T1 - Randomized parallel algorithms for trapezoidal diagrams

AU - Clarkson, Kenneth L.

AU - Cole, Richard

AU - Tarjan, Robert E.

PY - 1991/6/1

Y1 - 1991/6/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=77951880810&partnerID=8YFLogxK

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U2 - 10.1145/109648.109665

DO - 10.1145/109648.109665

M3 - Conference contribution

SN - 0897914260

VL - Part F129851

SP - 152

EP - 161

BT - Proceedings of the Annual Symposium on Computational Geometry

PB - Association for Computing Machinery

ER -