A nearly logarithmic lower bound on the randomized competitive ratio for the metrical task systems problem is presented. This implies a similar lower bound for the extensively studied K-server problem. The proof is based on Ramsey-type theorems for metric spaces, that state that every metric space contains a large subspace which is approximately a hierarchically well-separated tree (and in particular an ultrametric). These Ramsey-type theorems may be of independent interest.
Bibliographical noteFunding Information:
✩ A preliminary version, entitled “A Ramsey-type theorem for metric spaces and its applications for metrical task systems and related problems”, appeared in Proceedings of the 42nd Annual Symposium on Foundations of Computer Science, 2001. * Corresponding author. E-mail addresses: email@example.com (Y. Bartal), firstname.lastname@example.org (B. Bollobás), email@example.com, firstname.lastname@example.org (M. Mendel). 1 Supported in part by a grant from the Israeli Science Foundation (195/02). 2 Work mostly done while the author was a PhD student in Tel-Aviv University, under the supervision of Prof. A. Fiat. Author’s current address: Department of Computer Science, University of Illinois, Urbana, IL 61801, USA. Supported in part by a grant from the Israeli Science Foundation (195/02).
- Metric Ramsey theory
- Metric task systems
- Online servers problem