Journal of the ACM (JACM)
Information Processing Letters
Metrical Task Systems, the Server Problem and the Work Function Algorithm
Developments from a June 1996 seminar on Online algorithms: the state of the art
A general decomposition theorem for the k-server problem
Information and Computation
A General Decomposition Theorem for the k-Server Problem
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
Weak Adversaries for the k-Server Problem
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Randomized Competitive Analysis for Two-Server Problems
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
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In the k-Server Problem we wish to minimize, in an online fashion, the movement cost of k servers in response to a sequence of requests. The request issued at each step is specified by a point r in a given metric space M. To serve this request, one of the k servers must move to r. (We assume that k 驴 2.)It is known that if M has at least k + 1 points then no online algorithm for the k-Server Problem in M has competitive ratio smaller than k. The best known upper bound on the competitive ratio in arbitrary metric spaces, by Koutsoupias and Papadimitriou [6], is 2k-1. There is only a number of special cases for which k-competitive algorithms are known: for k = 2, when M is a tree, or when M has at most k + 2 points.The main result of this paper is that theWork Function Algorithm is 3-competitive for the 3-Server Problem in the Manhattan plane. As a corollary, we obtain a 4:243- competitive algorithm for 3 servers in the Euclidean plane. The best previously known competitive ratio for 3 servers in these spaces was 5.