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(log³ n log² k log log n) for any metric space on n points. Our algorithm improves upon the deterministic (2k-1)-competitive algorithm of Koutsoupias and Papadimitriou [J.ACM'95] whenever n is sub-exponential in k.