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.

• Type: Journal
• Year: 2006
• Where: JCSS
• Authors: Yair Bartal, Béla Bollobás, Manor Mendel
• Keywords: JCSS 2006, Logarithmic Lower Bound, Lower Bound, Metric Space