Competitive Algorithms for Maintaining a Mobile Center Sergey Bereg Email author Binay Bhattacharya David Kirkpatrick Michael Segal Article First Online: 31 March 2006 DOI :
10.1007/s11036-006-4470-z

Cite this article as: Bereg, S., Bhattacharya, B., Kirkpatrick, D. et al. Mobile Netw Appl (2006) 11: 177. doi:10.1007/s11036-006-4470-z
Abstract 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.

Preliminary versions of some of the results in this paper first appeared in the 4th International ACM Workshop on Discrete Algorithms and Methods for Mobile Computing and Communications (DIAL M for Mobility). This work has been supported by NSERC and MITACS. The work by Michael Segal was supported in part by the Pacific Institute for Mathematical Studies and REMON consortium.

Sergey Bereg received Ph.D. degree from Minsk Institute of Mathematics, Belarus in 1992. Dr. Bereg joined the Department of Computer Science at the University of Texas at Dallas in 2002 as an Associate Professor. He was a Visiting Professor at Duke University in 2001–2002. Prof. Bereg’s area of research is in Computational Geometry, Networks and Communications, Computational Biology. He is author of many journal and conference papers.

Binay Bhattacharya is a faculty member in the School of Computing Science at Simon Fraser University. His main research interest is in designing and developing geometric algorithms in various application areas. The application areas include, among others, geographical information systems, operations research.

David G. Kirkpatrick received his Ph.D. from the University of Toronto in 1974. He has been a faculty member in the Computer Science Department of the University of British Columbia since 1978 (as a Full Professor since 1986). Dr. Kirkpatrick is a founding Fellow of the British Columbia Advanced Systems Institute. His research interests include computational complexity, algorithmic combinatorics and computational geometry.

Michael Segal was born at October 12, 1972 in USSR. In 1991 he immigrated to Israel and started to study computer science in Ben-Gurion University of the Negev. He finished his B.Sc., M.Sc. and Ph.D. degrees in 1994, 1997, and 1999, respectively. During a period of 1999–2000 Dr. Michael Segal held a MITACS National Centre of Excellence Postdoctoral Fellow position in University of British Columbia, Canada. Dr. Segal joined the Department of Communication Systems Engineering, Ben-Gurion University, Israel in 2002 where he serves as department’s Chairman. His primary research is algorithms (sequential and distributed), data structures with applications to optimization problems, mobile wireless networks, communications and security.