Settling the Randomized k-sever Conjecture on Some Special Metrics

In this paper, we settle the randomized $k$-sever conjecture for the following metric spaces: line, circle, Hierarchically well-separated tree (HST). Specially, we show that there are $O(\log k)$-competitive randomized $k$-sever algorithms for above metric spaces. For any general metric space with $n$ points, we show that there is an $O( \log k \log n)$-competitive randomized $k$-sever algorithm.