A general decomposition theorem for the k-server problem
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This paper gives a nearly logarithmic lower bound on the randomized competitive ratio for the Metrical Task Systems model [9]. This implies a similar lower bound for the extensively studied K-server problem. Our proof is based on proving a Ramsey-type theorem for metric spaces. Inparticular we prove that in every metric space there exists a large subspace which is approximately a "hierarchically well-separated tree" (HST) [3]. This theorem may be of independent interest.