### Abstract

We study problems in computational geometry on PRAMs under the assumption that input objects are specified by points with O(log n)-bit coordinates, or, equivalently, with polynomially bounded integer coordinates. We show that in this setting many geometric problems can be solved in time O(log log n). The following five specific problems are investigated:closest pair of points, intersection of convex polygons, intersection of manhattan line segments, dominating set, and largest empty square. Algorithms solving them are developed which operate in time O(log log n) on the arbitrary CRCW PRAM. The number of processors used is either O(n) or O(n log n).

Original language | English (US) |
---|---|

Pages (from-to) | 52-69 |

Number of pages | 18 |

Journal | Algorithmica |

Volume | 14 |

Issue number | 1 |

DOIs | |

State | Published - Jul 1 1995 |

Externally published | Yes |

### Fingerprint

### Keywords

- Computational geometry
- Highly parallelizable problems
- PRAM

### ASJC Scopus subject areas

- Computer Science(all)
- Computer Science Applications
- Applied Mathematics

### Cite this

*Algorithmica*,

*14*(1), 52-69. https://doi.org/10.1007/BF01300373

**O(log log n)-time integer geometry on the CRCW PRAM.** / Chlebus, B. S.; Diks, K.; Kowaluk, M.

Research output: Contribution to journal › Article

*Algorithmica*, vol. 14, no. 1, pp. 52-69. https://doi.org/10.1007/BF01300373

}

TY - JOUR

T1 - O(log log n)-time integer geometry on the CRCW PRAM

AU - Chlebus, B. S.

AU - Diks, K.

AU - Kowaluk, M.

PY - 1995/7/1

Y1 - 1995/7/1

N2 - We study problems in computational geometry on PRAMs under the assumption that input objects are specified by points with O(log n)-bit coordinates, or, equivalently, with polynomially bounded integer coordinates. We show that in this setting many geometric problems can be solved in time O(log log n). The following five specific problems are investigated:closest pair of points, intersection of convex polygons, intersection of manhattan line segments, dominating set, and largest empty square. Algorithms solving them are developed which operate in time O(log log n) on the arbitrary CRCW PRAM. The number of processors used is either O(n) or O(n log n).

AB - We study problems in computational geometry on PRAMs under the assumption that input objects are specified by points with O(log n)-bit coordinates, or, equivalently, with polynomially bounded integer coordinates. We show that in this setting many geometric problems can be solved in time O(log log n). The following five specific problems are investigated:closest pair of points, intersection of convex polygons, intersection of manhattan line segments, dominating set, and largest empty square. Algorithms solving them are developed which operate in time O(log log n) on the arbitrary CRCW PRAM. The number of processors used is either O(n) or O(n log n).

KW - Computational geometry

KW - Highly parallelizable problems

KW - PRAM

UR - http://www.scopus.com/inward/record.url?scp=34249761270&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34249761270&partnerID=8YFLogxK

U2 - 10.1007/BF01300373

DO - 10.1007/BF01300373

M3 - Article

AN - SCOPUS:34249761270

VL - 14

SP - 52

EP - 69

JO - Algorithmica

JF - Algorithmica

SN - 0178-4617

IS - 1

ER -