Abstract
We show that the Harmonic algorithm for the online K-server problem is ( ~11 x 2K – 2K)competitive against an adaptive online adversary for K 22. From a result of [BBKTW90], we get a deterministic algorithm which is ( ~K x 2K – 2102competitive. These are the best competitive ratios that have been published so far for online algorithms over a general metric space when K >2.

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