Polylog(n)-competitive algorithm for metrical task systems

Yair Bartal*, Avrim Blum, Carl Burch, Andrew Tomkins

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

72 Scopus citations


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 languageAmerican English
Pages (from-to)711-719
Number of pages9
JournalConference Proceedings of the Annual ACM Symposium on Theory of Computing
StatePublished - 1997
Externally publishedYes
EventProceedings of the 1997 29th Annual ACM Symposium on Theory of Computing - El Paso, TX, USA
Duration: 4 May 19976 May 1997


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