On the Fermat-Weber center of a convex object

Paz Carmi; Sariel Har-Peled; Matthew J. Katz

doi:10.1016/j.comgeo.2005.01.002

On the Fermat-Weber center of a convex object

Paz Carmi, Sariel Har-Peled, Matthew J. Katz

Computer Science

Research output: Contribution to journal › Article › peer-review

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)
Pages (from-to)	188-195
Number of pages	8
Journal	Computational Geometry: Theory and Applications
Volume	32
Issue number	3
DOIs	https://doi.org/10.1016/j.comgeo.2005.01.002
State	Published - Nov 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

Online availability

10.1016/j.comgeo.2005.01.002

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title = "On the Fermat-Weber center of a convex object",

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.",

keywords = "Approximation algorithms, Fermat-Weber center",

author = "Paz Carmi and Sariel Har-Peled and Katz, {Matthew J.}",

note = "Funding Information: * Corresponding author. E-mail addresses: carmip@cs.bgu.ac.il (P. Carmi), sariel@cs.uiuc.edu (S. Har-Peled), matya@cs.bgu.ac.il (M.J. Katz). URL: http://www.uiuc.edu/~sariel/ (S. Har-Peled). 1 Partially supported by grant no. 2000160 from the US–Israel Binational Science Foundation, and by a Kreitman Foundation doctoral fellowship. 2 Partially supported by a NSF CAREER award CCR-0132901. 3 Partially supported by grant no. 2000160 from the US–Israel Binational Science Foundation.",

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doi = "10.1016/j.comgeo.2005.01.002",

language = "English (US)",

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AU - Har-Peled, Sariel

AU - Katz, Matthew J.

N1 - Funding Information: * Corresponding author. E-mail addresses: carmip@cs.bgu.ac.il (P. Carmi), sariel@cs.uiuc.edu (S. Har-Peled), matya@cs.bgu.ac.il (M.J. Katz). URL: http://www.uiuc.edu/~sariel/ (S. Har-Peled). 1 Partially supported by grant no. 2000160 from the US–Israel Binational Science Foundation, and by a Kreitman Foundation doctoral fellowship. 2 Partially supported by a NSF CAREER award CCR-0132901. 3 Partially supported by grant no. 2000160 from the US–Israel Binational Science Foundation.

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Y1 - 2005/11

N2 - 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.

AB - 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.

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KW - Fermat-Weber center

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On the Fermat-Weber center of a convex object

Abstract

Keywords

ASJC Scopus subject areas

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