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: [email protected] (P. Carmi), [email protected] (S. Har-Peled), [email protected] (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 -