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

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.Comment: Fix an error in the metadata. 31 pages, 0 figures. Preliminary version in FOCS '01. To be published in J. Comput. System Sc