### Abstract

We show that for any convex object Q in the plane, the average distance from the Fermat-Weber center of Q to the points in Q is at least Δ(Q)/7, where Δ(Q) is the diameter of Q, and that there exists a convex object P for which this distance is Δ(P)/6. We use this result to obtain a linear-time approximation scheme for finding an approximate Fermat-Weber center of a convex polygon Q.

Original language | English (US) |
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Pages (from-to) | 188-195 |

Number of pages | 8 |

Journal | Computational Geometry: Theory and Applications |

Volume | 32 |

Issue number | 3 |

DOIs | |

State | Published - Nov 1 2005 |

### Keywords

- Approximation algorithms
- Fermat-Weber center

### ASJC Scopus subject areas

- Computer Science Applications
- Geometry and Topology
- Control and Optimization
- Computational Theory and Mathematics
- Computational Mathematics

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## Cite this

Carmi, P., Har-Peled, S., & Katz, M. J. (2005). On the Fermat-Weber center of a convex object.

*Computational Geometry: Theory and Applications*,*32*(3), 188-195. https://doi.org/10.1016/j.comgeo.2005.01.002