## Abstract

We present a randomized on-line algorithm for the Metrical Task System problem that achieves a competitive ratio of O(log^{6} 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(log^{2} n)-competitive algorithm for Ω(log^{2} 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(c^{6} log^{6} k).

Original language | American English |
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Pages (from-to) | 711-719 |

Number of pages | 9 |

Journal | Conference Proceedings of the Annual ACM Symposium on Theory of Computing |

State | Published - 1997 |

Externally published | Yes |

Event | Proceedings of the 1997 29th Annual ACM Symposium on Theory of Computing - El Paso, TX, USA Duration: 4 May 1997 → 6 May 1997 |