Ramsey-type theorems for metric spaces with applications to online problems

Yair Bartal*, Béla Bollobás, Manor Mendel

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

45 Scopus citations

Abstract

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.

Original languageAmerican English
Pages (from-to)890-921
Number of pages32
JournalJournal of Computer and System Sciences
Volume72
Issue number5
DOIs
StatePublished - Aug 2006

Bibliographical note

Funding 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 protected] (Y. Bartal), [email protected] (B. Bollobás), [email protected], [email protected] (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).

Keywords

  • Metric Ramsey theory
  • Metric task systems
  • Online servers problem

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