Bereg, S., Bhattacharya, B., Kirkpatrick, D. et al. Mobile Netw Appl (2006) 11: 177. doi:10.1007/s11036-006-4470-z
In this paper we investigate the problem of locating a mobile facility at (or near) the center of a set of clients that move independently, continuously, and with bounded velocity. It is shown that the Euclidean 1-center of the clients may move with arbitrarily high velocity relative to the maximum client velocity. This motivates the search for strategies for moving a facility so as to closely approximate the Euclidean 1-center while guaranteeing low (relative) velocity.
We present lower bounds and efficient competitive algorithms for the exact and approximate maintenance of the Euclidean 1-center for a set of moving points in the plane. These results serve to accurately quantify the intrinsic velocity approximation quality tradeoff associated with the maintenance of the mobile Euclidean 1-center.