A decomposition theorem and bounds for randomized server problems

The authors prove a lower bound of Ω(√logk/loglogk) for the competitive ratio of randomized algorithms for the k-server problem against an oblivious adversary. The bound holds for arbitrary metric spaces (of at least k+1 points) and provides a new lower bound for the metrical task system problem as well. This improves the previous best lower bound of Ω(loglogk) for arbitrary metric spaces, more closely approaching the conjectured lower bound of Ω(logk ). They also prove a lower bound of Ω(^logk/_loglogk) for the server problem on k+1 equally-spaced points on a line, which corresponds to some natural motion-planning problems