A polylog(n)-competitive algorithm for metrical task systems

We present a randomized on-line algorithm for the Metrical Task System problem that achieves a competitive ratio of O(log6 n) for arbitrary metric spaces, against an oblivious adversary. This is the first algorithm to achieve a sublinear competitive ratio for all metric spaces. Our algorit hm uses a recent result of Bartal [Bar96] that an arbitrary metr ic space can be probabilistically approximated by a set of metric spaces called “ k-hierarchical well-separated trees” ( kHST’s). Indeed, the main technical result of this paper is an O(log2 n)-competitive algorithm for (log2 n)-HST spaces. This, combined with the result of [Bar96], yields the genera l bound. Note that for thek-server problem on metric spaces of k + c points our result implies a competitive ratio of O(c6 log6 k).

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