TY - JOUR

T1 - On the Fermat-Weber center of a convex object

AU - Carmi, Paz

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.

PY - 2005/11/1

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 - http://www.scopus.com/inward/record.url?scp=84867949402&partnerID=8YFLogxK

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

SP - 188

EP - 195

JO - Computational Geometry: Theory and Applications

JF - Computational Geometry: Theory and Applications

IS - 3

ER -