Amortized efficiency of list update and paging rules
Communications of the ACM
Competitive algorithms for server problems
Journal of Algorithms
Approximation algorithms for geometric median problems
Information Processing Letters
An efficient algorithm for the Euclidean two-center problem
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Approximation schemes for Euclidean k-medians and related problems
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Kinetic data structures: a state of the art report
WAFR '98 Proceedings of the third workshop on the algorithmic foundations of robotics on Robotics : the algorithmic perspective: the algorithmic perspective
A constant-factor approximation algorithm for the k-median problem (extended abstract)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Faster construction of planar two-centers
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Data structures for mobile data
Journal of Algorithms
Mobile facility location (extended abstract)
DIALM '00 Proceedings of the 4th international workshop on Discrete algorithms and methods for mobile computing and communications
Maintaining approximate extent measures of moving points
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Improved Combinatorial Algorithms for the Facility Location and k-Median Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Primal-Dual Approximation Algorithms for Metric Facility Location and k-Median Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Geometric optimization and computational complexity (algebra, algorithms, robotics)
Geometric optimization and computational complexity (algebra, algorithms, robotics)
Kinetic data structures
Deformable spanners and applications
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Discrete & Computational Geometry
Kinetic maintenance of mobile k-centres on trees
Discrete Applied Mathematics
Minimum enclosing circle of a set of fixed points and a mobile point
WALCOM'11 Proceedings of the 5th international conference on WALCOM: algorithms and computation
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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.