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arXiv · cs/0406028

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

Yair Bartal·Bela Bollobas·Manor Mendel
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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.

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Yair Bartal, Bela Bollobas, Manor Mendel. 2004-06-16. Ramsey-type theorems for metric spaces with applications to online problems. https://doi.org/10.1016/j.jcss.2005.05.008

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