Ramsey-type theorems for metric spaces with applications to online problems
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. © 2006 Elsevier Inc. All rights reserved.
Journal of Computer and System Sciences
Bartal, Y., Bollobás, B., & Mendel, M. (2006). Ramsey-type theorems for metric spaces with applications to online problems. Journal of Computer and System Sciences, 72 (5), 890-921. https://doi.org/10.1016/j.jcss.2005.05.008