### Abstract

We present a parMlel algorithm for the Voronoi diagram of the set of vertices of a convex polygon. The algorithm runs in time O(log n) and uses O(nloglog n/log n) processors in the CRCW PRAM model. The concurrent write is used only by an integer sorting subroutine. We also obtain an O(log n)-time and O(n log log n log n)-proceor CRCW PRAM algorithm for the construction of the medial axis of a convex polygon. Our algorithms use the solution to the duration-unknown task scheduling problem due to Cole and Vishkin and the optimal parallel algorithm for the convex hull of a polygon due to Wagener. They are randomized in the sense that for any given I > 0 they terminate in time O(log n) with probability greater than 1-n ^{-1}.

Original language | English (US) |
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Title of host publication | Algorithm Theory – SWAT 1994 - 4th Scandinavian Workshop on Algorithm Theory, Proceedings |

Editors | Erik M. Schmidt, Sven Skyum |

Publisher | Springer Verlag |

Pages | 73-82 |

Number of pages | 10 |

ISBN (Print) | 9783540582182 |

DOIs | |

State | Published - 1994 |

Event | 4th Scandinavian Workshop on Algorithm Theory, SWAT 1994 - Aarhus, Denmark Duration: Jul 6 1994 → Jul 8 1994 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 824 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 4th Scandinavian Workshop on Algorithm Theory, SWAT 1994 |
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Country | Denmark |

City | Aarhus |

Period | 7/6/94 → 7/8/94 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Algorithm Theory – SWAT 1994 - 4th Scandinavian Workshop on Algorithm Theory, Proceedings*(pp. 73-82). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 824 LNCS). Springer Verlag. https://doi.org/10.1007/3-540-58218-5_7