### Abstract

For any set X of points (in any dimension) and any k= 1, 2,..., we introduce the concept of the k-bull of X. This unifies the well-known notion of 'convex hulls with the notion of 'centers' recently introduced by F.F. Yao. The concept is intimately related to some other concepts (k-belts, k-sets) studied by Edelsbronner, Welzl, Lovász, Erdös and others. Several computational problems related to k-hulls are studied here. Some of our algorithms are of interest in themselves because of the techniques employed; in particular, the 'parametric' searching technique of Megiddo is used in a non- Trivial way. We will also extend Megiddo's technique to Las Vegas algorithms. Our results have applications to a variety of problems in computational geometry: efficient computation of the 'cut∗ guaranteed by the classical 'Ham Sandwich theorem', faster preprocessing time for polygon retrieval, and theoretical improvements to a problem of intersecting lines and points posed by Hopcroft.

Original language | English (US) |
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Title of host publication | Proceedings of the 16th Annual ACM Symposium on Theory of Computing, STOC 1984 |

Publisher | Association for Computing Machinery |

Pages | 154-166 |

Number of pages | 13 |

ISBN (Electronic) | 0897911334 |

DOIs | |

State | Published - Dec 1 1984 |

Event | 16th Annual ACM Symposium on Theory of Computing, STOC 1984 - Washington, United States Duration: Apr 30 1984 → May 2 1984 |

### Publication series

Name | Proceedings of the Annual ACM Symposium on Theory of Computing |
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ISSN (Print) | 0737-8017 |

### Other

Other | 16th Annual ACM Symposium on Theory of Computing, STOC 1984 |
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Country | United States |

City | Washington |

Period | 4/30/84 → 5/2/84 |

### ASJC Scopus subject areas

- Software

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## Cite this

*Proceedings of the 16th Annual ACM Symposium on Theory of Computing, STOC 1984*(pp. 154-166). (Proceedings of the Annual ACM Symposium on Theory of Computing). Association for Computing Machinery. https://doi.org/10.1145/800057.808677