A General Decomposition Theorem for the k-Server Problem

The first general decomposition theorem for the k-server problem is presented. Whereas all previous theorems are for the case of a finite metric with k + 1 points, the theorem given here allows an arbitrary number of points in the underlying metric space. This theorem implies O(polylog(k))-competitive algorithms for certain metric spaces consisting of a polylogarithmic number of widely separated sub-spaces. The only other cases for which polylogarithmic competitive algorithms are known are the uniform metric space, and the weighted cache metric space with two weights.