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

Authors:
Yair Bartal;Béla Bollobás;Manor Mendel
Affiliations:
Hebrew University, Jerusalem, Israel;University of Memphis, Memphis, TN;Department of Computer Science, University of Illinois, Urbana, IL and Hebrew University, Jerusalem, Israel and Tel-Aviv University
Venue:
Journal of Computer and System Sciences - Special issue on FOCS 2001
Year:
2006

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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.