A Polylogarithmic-Competitive Algorithm for the k-Server Problem

We give the first polylogarithmic-competitive randomized online algorithm for the k-server problem on an arbitrary finite metric space. In particular, our algorithm achieves a competitive ratio of (O) over tilde (log(3) n log(2) k) for any metric space on n points. Our algorithm improves upon the deterministic (2k - 1)-competitive algorithm of Koutsoupias and Papadimitriou [Koutsoupias and Papadimitriou 1995] for a wide range of n.