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In this paper, we show that there is an O(log k log^2 n)-competitiverandomized algorithm for the k-sever problem on any metric space with n points,which improved the previous best competitive ratio O(log^2 k log^3 n log log n)by Nikhil Bansal et al. (FOCS 2011, pages 267-276).

An O(log k log^2 n)-competitive Randomized Algorithm for the k-Sever Problem