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(log^3 n log^2 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. 
Nikhil Bansal, Niv Buchbinder, Aleksander Madry, Joseph (Seffi) Naor
cs.DS