Improved bounds on the average distance to the Fermat--Weber center of a convex object

Authors:
A. Karim Abu-Affash;Matthew J. Katz
Affiliations:
Department of Computer Science, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel;Department of Computer Science, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel
Venue:
Information Processing Letters
Year:
2009

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Abstract

We show that for any convex object Q in the plane, the average distance between the Fermat-Weber center of Q and the points in Q is at least 4@D(Q)/25, and at most 2@D(Q)/(33), where @D(Q) is the diameter of Q. We use the former bound to improve the approximation ratio of a load-balancing algorithm of Aronov et al. [B. Aronov, P. Carmi, M.J. Katz, Minimum-cost load-balancing partitions, Algorithmica, in press].