Improved Bounds on the Average Distance to the Fermat-Weber Center of a Convex Object
A. Karim, A. Karim Abu-Affash, J. Katz · 2014
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. [1]. 1