The k-server problem is a fundamental online problem where k mobile servers should be scheduled to answer a sequence of requests for points in a metric space as to minimize the total movement cost. While the deterministic competitive ratio is at least k, randomized k-server algorithms have the potential of reaching o(k)-competitive ratios. Prior to this work only few specific cases of this problem were solved. For arbitrary metric spaces, this goal may be approached by using probabilistic metric approximation techniques. This paper gives the first results in this direction, obtaining o(k)-competitive ratio for a natural class of metric spaces, including d-dimensional grids, and wide range of k.
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✩ A preliminary version of this work appears in Proceedings of the 15th Annual ACM–SIAM Symposium on Discrete Algorithms, 2004, pp. 659–664. * Corresponding author. E-mail addresses: email@example.com (Y. Bartal), firstname.lastname@example.org (M. Mendel). 1 Supported in part by a grant from the Israeli Science Foundation (195/02). 2 Supported in part by the Landau Center.