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 algorithm uses a recent result of Bartal [Bar96] that an arbitrary metric space can be probabilistically approximated by a set of metric spaces called `k-hierarchical well-separated trees' (k-HST's). Indeed, the main technical result of this paper is an O(log2 n)-competitive algorithm for Ω(log2 n)-HST spaces. This, combined with the result of [Bar96], yields the general bound. Note that for the k-server problem on metric spaces of k+c points our result implies a competitive ratio of O(c6 log6 k).
|Original language||American English|
|Number of pages||9|
|Journal||Conference Proceedings of the Annual ACM Symposium on Theory of Computing|
|State||Published - 1997|
|Event||Proceedings of the 1997 29th Annual ACM Symposium on Theory of Computing - El Paso, TX, USA|
Duration: 4 May 1997 → 6 May 1997