## 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 |
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Pages (from-to) | 505-514 |

Number of pages | 10 |

Journal | Parallel Computing |

Volume | 17 |

Issue number | 4-5 |

DOIs | |

Publication status | Published - 1991 Jul |

Externally published | Yes |

## Keywords

- Parallel algorithm
- Voronoi diagram
- mesh-connected computer

## ASJC Scopus subject areas

- Software
- Theoretical Computer Science
- Hardware and Architecture
- Computer Networks and Communications
- Computer Graphics and Computer-Aided Design
- Artificial Intelligence