### Abstract

Let P be a set of n points in the plane and let e be a segment of fixed length. The segment center problem is to find a placement of e (allowing translation and rotation) that minimizes the maximum euclidean distance from e to the points of P. We present an algorithm that solves the problem in time O(n log^{4} n log log n), improving the previous solution of Agarwal et al. by nearly a factor of O(n).

Original language | English (US) |
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Title of host publication | Proceedings of the Annual ACM SIAM Symposium on Discrete Algorithms |

Publisher | Publ by ACM |

Pages | 87-97 |

Number of pages | 11 |

ISBN (Print) | 0898713293 |

State | Published - Jan 1 1994 |

Externally published | Yes |

Event | Proceedings of the Fifth Annual SIAM Symposium on Discrete Algorithms - Arlington, VA, USA Duration: Jan 23 1994 → Jan 25 1994 |

### Publication series

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

Other | Proceedings of the Fifth Annual SIAM Symposium on Discrete Algorithms |
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City | Arlington, VA, USA |

Period | 1/23/94 → 1/25/94 |

### ASJC Scopus subject areas

- Software
- Mathematics(all)

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## Cite this

Efrat, A., & Sharir, M. (1994). Near-linear algorithm for the planar segment center problem. In

*Proceedings of the Annual ACM SIAM Symposium on Discrete Algorithms*(pp. 87-97). (Proceedings of the Annual ACM SIAM Symposium on Discrete Algorithms). Publ by ACM.