### 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) which minimizes the maximum euclidean distance from e to the points of P. We present an algorithm that solves the problem in time O(n^{1+ε}), for any ε > 0, improving the previous solution of Agarwal et al. [3] by nearly a factor of O(n).

Original language | English (US) |
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Pages (from-to) | 239-257 |

Number of pages | 19 |

Journal | Discrete and Computational Geometry |

Volume | 16 |

Issue number | 3 |

DOIs | |

State | Published - Oct 1996 |

Externally published | Yes |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics

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## Cite this

Efrat, A., & Sharir, M. (1996). A near-linear algorithm for the planar segment-center problem.

*Discrete and Computational Geometry*,*16*(3), 239-257. https://doi.org/10.1007/BF02711511