### Abstract

Given a family of objects in the plane, the line transversal problem is to compute a line that intersects every member of the family. In this paper we examine a variation of the line transversal problem that involves computing a shortest line segment that intersects every member of the family. In particular, we give O(nlogn) time algorithms for computing a shortest transversal of a family of n lines and of a family of n line segments. We also present an O(n log^{2} n) time algorithm for computing a shortest transversal of a family of polygons with a total of n vertices. In general, finding a line transversal for a family of n objects takes Ω(n log n) time. This time bound holds for a family of n line segments thus our shortest transversal algorithm for this family is optimal.

Original language | English (US) |
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Title of host publication | Proceedings of the Annual Symposium on Computational Geometry |

Publisher | Association for Computing Machinery |

Pages | 71-80 |

Number of pages | 10 |

ISBN (Print) | 0897914260 |

DOIs | |

State | Published - Jun 1 1991 |

Event | 7th Annual Symposium on Computational Geometry, SCG 1991 - North Conway, United States Duration: Jun 10 1991 → Jun 12 1991 |

### Publication series

Name | Proceedings of the Annual Symposium on Computational Geometry |
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### Other

Other | 7th Annual Symposium on Computational Geometry, SCG 1991 |
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Country | United States |

City | North Conway |

Period | 6/10/91 → 6/12/91 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Geometry and Topology
- Computational Mathematics

### Cite this

*Proceedings of the Annual Symposium on Computational Geometry*(pp. 71-80). (Proceedings of the Annual Symposium on Computational Geometry). Association for Computing Machinery. https://doi.org/10.1145/109648.109656