Improved Bounds on the Average Distance to the Fermat-Weber Center of a Convex Object

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(Q)/25, and at most 2(Q)/(3 3), where (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. [2].

• Type: Conference
• Year: 2008
• Where: CCCG
• Authors: A. Karim Abu-Affash, Matthew J. Katz
• Keywords: Average Distance, CCCG 2008, Computational Geometry, Convex Object, Fermat-Weber Center