### Abstract

We show that a number of geometric problems can be solved on a √n × √n mesh-connected computer (MCC) in O(√n) time, which is optimal to within a constant factor, since a nontrivial data movement on an MCC requires Ω(√n) time. The problems studied here include multipoint location, planar point location, trapezoidal decomposition, intersection detection, intersection of two convex polygons, Voronoi diagram, the largest empty circle, the smallest enclosing circle, etc. The O(√n) algorithms for all of the above problems are based on the classical divide-and-conquer problem-solving strategy.

Original language | English |
---|---|

Pages (from-to) | 155-177 |

Number of pages | 23 |

Journal | Algorithmica (New York) |

Volume | 5 |

Issue number | 2 |

Publication status | Published - 1990 Jan 1 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Computer Graphics and Computer-Aided Design
- Software
- Safety, Risk, Reliability and Quality
- Applied Mathematics

### Cite this

*Algorithmica (New York)*,

*5*(2), 155-177.

**Parallel geometric algorithms on a mesh-connected computer.** / Jeong, Chang-Sung; Lee, D. T.

Research output: Contribution to journal › Article

*Algorithmica (New York)*, vol. 5, no. 2, pp. 155-177.

}

TY - JOUR

T1 - Parallel geometric algorithms on a mesh-connected computer

AU - Jeong, Chang-Sung

AU - Lee, D. T.

PY - 1990/1/1

Y1 - 1990/1/1

N2 - We show that a number of geometric problems can be solved on a √n × √n mesh-connected computer (MCC) in O(√n) time, which is optimal to within a constant factor, since a nontrivial data movement on an MCC requires Ω(√n) time. The problems studied here include multipoint location, planar point location, trapezoidal decomposition, intersection detection, intersection of two convex polygons, Voronoi diagram, the largest empty circle, the smallest enclosing circle, etc. The O(√n) algorithms for all of the above problems are based on the classical divide-and-conquer problem-solving strategy.

AB - We show that a number of geometric problems can be solved on a √n × √n mesh-connected computer (MCC) in O(√n) time, which is optimal to within a constant factor, since a nontrivial data movement on an MCC requires Ω(√n) time. The problems studied here include multipoint location, planar point location, trapezoidal decomposition, intersection detection, intersection of two convex polygons, Voronoi diagram, the largest empty circle, the smallest enclosing circle, etc. The O(√n) algorithms for all of the above problems are based on the classical divide-and-conquer problem-solving strategy.

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UR - http://www.scopus.com/inward/citedby.url?scp=0025211481&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0025211481

VL - 5

SP - 155

EP - 177

JO - Algorithmica

JF - Algorithmica

SN - 0178-4617

IS - 2

ER -