A Ramsey-type theorem for metric spaces and its applications for Metrical Task Systems and related problems

Yair Bartal; Béla Bollobás; Manor Mendel

doi:10.1109/SFCS.2001.959914

A Ramsey-type theorem for metric spaces and its applications for Metrical Task Systems and related problems

Yair Bartal, Béla Bollobás, Manor Mendel

Research output: Contribution to journal › Article › peer-review

Abstract

This paper gives a nearly logarithmic lower bound on the randomized competitive ratio for the Metrical Task Systems model. This implies a similar lower bound for the extensively studied K-server problem. Our proof is based on proving a Ramsey-type theorem for metric spaces. In particular we prove that in every metric space there exists a large subspace which is approximately a "hierarchically well-separated tree" (HST). This theorem may be of independent interest.

Original language	English
Pages (from-to)	396-405
Number of pages	10
Journal	Annual Symposium on Foundations of Computer Science - Proceedings
DOIs	https://doi.org/10.1109/SFCS.2001.959914
State	Published - 2001
Externally published	Yes

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10.1109/SFCS.2001.959914

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abstract = "This paper gives a nearly logarithmic lower bound on the randomized competitive ratio for the Metrical Task Systems model. This implies a similar lower bound for the extensively studied K-server problem. Our proof is based on proving a Ramsey-type theorem for metric spaces. In particular we prove that in every metric space there exists a large subspace which is approximately a {"}hierarchically well-separated tree{"} (HST). This theorem may be of independent interest.",

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A Ramsey-type theorem for metric spaces and its applications for Metrical Task Systems and related problems

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