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In this paper we give deterministic competitive k-server algorithms for all k and all metric spaces. This settles the k-server conjecture up to the competitive ratio, The best previous result for general metric spaces was a three-server randomized competitive algorithm and a nonconstructive proof that a deterministic three-server competitive algorithm exists. The competitive ratio we can prove is exponential in the number of servers. Thus, the question of the minimal competitive ratio for arbitrary metric spaces is still open.doi:10.1016/s0022-0000(05)80060-1 fatcat:ubdqin3jq5eqtptdlfampocfca