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

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

20 Scopus citations

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
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 - 1 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

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10.1016/j.comgeo.2005.01.002

Cite this

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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.",

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AU - Carmi, Paz

AU - Har-Peled, Sariel

AU - Katz, Matthew J.

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Y1 - 2005/11/1

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.

KW - Approximation algorithms

KW - Fermat-Weber center

UR - https://www.scopus.com/pages/publications/84867949402

U2 - 10.1016/j.comgeo.2005.01.002

DO - 10.1016/j.comgeo.2005.01.002

M3 - Article

AN - SCOPUS:84867949402

SN - 0925-7721

VL - 32

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EP - 195

JO - Computational Geometry: Theory and Applications

JF - Computational Geometry: Theory and Applications

IS - 3

ER -

On the Fermat-Weber center of a convex object

Abstract

Keywords

ASJC Scopus subject areas

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