### Abstract

In this paper, we give an algorithm for output-sensitn construction of an f-face polytope that is defined by halfspaces in E^{4}. Our algorithm runs in O((n + /)log^{2} ) time and uses 0(n + f) space. This is the first algorithi within a polylogarithmic factor of optimal 0(n logf/ + f) time over the whole range of f. By a standard liftir map, we obtain output-sensitive algorithms for the Voroni diagram or Delaunay triangulation in E^{3} and for the portic of a Voronoi diagram that is clipped to a convex polytop Our approach also simplifies the "ultimate convex hn algorithm" of Kirkpatrick and Seidel in E^{2}.

Original language | English (US) |
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Title of host publication | Proceedings of the 6th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1995 |

Publisher | Association for Computing Machinery |

Pages | 282-291 |

Number of pages | 10 |

ISBN (Electronic) | 0898713498 |

State | Published - Jan 22 1995 |

Event | 6th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1995 - San Francisco, United States Duration: Jan 22 1995 → Jan 24 1995 |

### Publication series

Name | Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms |
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### Other

Other | 6th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1995 |
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Country | United States |

City | San Francisco |

Period | 1/22/95 → 1/24/95 |

### Fingerprint

### ASJC Scopus subject areas

- Software
- Mathematics(all)

### Cite this

*Proceedings of the 6th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1995*(pp. 282-291). (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms). Association for Computing Machinery.