### 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 |

Volume | Part F129851 |

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 |

### 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*(Vol. Part F129851, pp. 71-80). Association for Computing Machinery. https://doi.org/10.1145/109648.109656

**Computing shortest transversals of sets.** / Bhattacharya, Binay; Czyzowicz, Jurek; Egyed, Peter; Stojmenovic, Ivan; Toussaint, Godfried; Urrutia, Jorge.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the Annual Symposium on Computational Geometry.*vol. Part F129851, Association for Computing Machinery, pp. 71-80, 7th Annual Symposium on Computational Geometry, SCG 1991, North Conway, United States, 6/10/91. https://doi.org/10.1145/109648.109656

}

TY - GEN

T1 - Computing shortest transversals of sets

AU - Bhattacharya, Binay

AU - Czyzowicz, Jurek

AU - Egyed, Peter

AU - Stojmenovic, Ivan

AU - Toussaint, Godfried

AU - Urrutia, Jorge

PY - 1991/6/1

Y1 - 1991/6/1

N2 - 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 log2 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.

AB - 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 log2 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.

UR - http://www.scopus.com/inward/record.url?scp=79951674611&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79951674611&partnerID=8YFLogxK

U2 - 10.1145/109648.109656

DO - 10.1145/109648.109656

M3 - Conference contribution

SN - 0897914260

VL - Part F129851

SP - 71

EP - 80

BT - Proceedings of the Annual Symposium on Computational Geometry

PB - Association for Computing Machinery

ER -