### 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 |

Volume | 5 |

Issue number | 1-4 |

DOIs | |

Publication status | Published - 1990 Jun 1 |

Externally published | Yes |

### Fingerprint

### Keywords

- Computational geometry
- Mesh-connected computer
- Multipoint location
- Parallel algorithms
- Voronoi diagrams

### ASJC Scopus subject areas

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

### Cite this

*Algorithmica*,

*5*(1-4), 155-177. https://doi.org/10.1007/BF01840383

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

Research output: Contribution to journal › Article

*Algorithmica*, vol. 5, no. 1-4, pp. 155-177. https://doi.org/10.1007/BF01840383

}

TY - JOUR

T1 - Parallel geometric algorithms on a mesh-connected computer

AU - Jeong, Chang-Sung

AU - Lee, D. T.

PY - 1990/6/1

Y1 - 1990/6/1

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.

KW - Computational geometry

KW - Mesh-connected computer

KW - Multipoint location

KW - Parallel algorithms

KW - Voronoi diagrams

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UR - http://www.scopus.com/inward/citedby.url?scp=52449146405&partnerID=8YFLogxK

U2 - 10.1007/BF01840383

DO - 10.1007/BF01840383

M3 - Article

VL - 5

SP - 155

EP - 177

JO - Algorithmica

JF - Algorithmica

SN - 0178-4617

IS - 1-4

ER -