### Abstract

While constructing a Voronoi diagram V
_{P} for a set P of n points on a mesh-connected computer (MCC), it is necessary to find a set B of edges which are intersected by the dividing chain C during the merge process of two Voronoi diagrams V
_{L} and V
_{R}, where L and R contain the leftmost [n/2] points and the rightmost [n/2] points of P respectively. The computation of B requires two operations: First decide for each edge e in V
_{L} and V
_{R} whether its end vertices are closer to L or R, and then from that information, determine whether e is intersected by C. However, in the previous parallel algorithm each of the former and latter operations requires planar point location which takes O(√n) time on a √n × √n MCC, and in addition the former operation needs to compute convex hulls of L and R. In this paper, we shall show that the latter operation can be done in O(1) time without executing planar point location and the former operation can be executed without the computation of convex hulls. Therefore, the computation of B is reduced to only one planar point location.

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

Pages (from-to) | 505-514 |

Number of pages | 10 |

Journal | Parallel Computing |

Volume | 17 |

Issue number | 4-5 |

Publication status | Published - 1991 Jul 1 |

Externally published | Yes |

### Fingerprint

### Keywords

- mesh-connected computer
- Parallel algorithm
- Voronoi diagram

### ASJC Scopus subject areas

- Computer Science Applications
- Hardware and Architecture
- Control and Systems Engineering

### Cite this

**An improved parallel algorithm for constructing voronoi diagram on a mesh-connected computer.** / Jeong, Chang-Sung.

Research output: Contribution to journal › Article

*Parallel Computing*, vol. 17, no. 4-5, pp. 505-514.

}

TY - JOUR

T1 - An improved parallel algorithm for constructing voronoi diagram on a mesh-connected computer

AU - Jeong, Chang-Sung

PY - 1991/7/1

Y1 - 1991/7/1

N2 - While constructing a Voronoi diagram V P for a set P of n points on a mesh-connected computer (MCC), it is necessary to find a set B of edges which are intersected by the dividing chain C during the merge process of two Voronoi diagrams V L and V R, where L and R contain the leftmost [n/2] points and the rightmost [n/2] points of P respectively. The computation of B requires two operations: First decide for each edge e in V L and V R whether its end vertices are closer to L or R, and then from that information, determine whether e is intersected by C. However, in the previous parallel algorithm each of the former and latter operations requires planar point location which takes O(√n) time on a √n × √n MCC, and in addition the former operation needs to compute convex hulls of L and R. In this paper, we shall show that the latter operation can be done in O(1) time without executing planar point location and the former operation can be executed without the computation of convex hulls. Therefore, the computation of B is reduced to only one planar point location.

AB - While constructing a Voronoi diagram V P for a set P of n points on a mesh-connected computer (MCC), it is necessary to find a set B of edges which are intersected by the dividing chain C during the merge process of two Voronoi diagrams V L and V R, where L and R contain the leftmost [n/2] points and the rightmost [n/2] points of P respectively. The computation of B requires two operations: First decide for each edge e in V L and V R whether its end vertices are closer to L or R, and then from that information, determine whether e is intersected by C. However, in the previous parallel algorithm each of the former and latter operations requires planar point location which takes O(√n) time on a √n × √n MCC, and in addition the former operation needs to compute convex hulls of L and R. In this paper, we shall show that the latter operation can be done in O(1) time without executing planar point location and the former operation can be executed without the computation of convex hulls. Therefore, the computation of B is reduced to only one planar point location.

KW - mesh-connected computer

KW - Parallel algorithm

KW - Voronoi diagram

UR - http://www.scopus.com/inward/record.url?scp=0026188214&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0026188214&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0026188214

VL - 17

SP - 505

EP - 514

JO - Parallel Computing

JF - Parallel Computing

SN - 0167-8191

IS - 4-5

ER -