# A polylog(n)-competitive algorithm for metrical task systems

@inproceedings{Bartal1997APA,
title={A polylog(n)-competitive algorithm for metrical task systems},
author={Yair Bartal and Avrim Blum and Carl Burch and Andrew Tomkins},
booktitle={Symposium on the Theory of Computing},
year={1997}
}
• Published in
Symposium on the Theory of…
4 May 1997
• Computer Science, Mathematics
We present a randomized on-line algorithm for the Metrical Task System problem that achieves a competitive ratio of O(log6 n) for arbitrary metric spaces, against an oblivious adversary. This is the first algorithm to achieve a sublinear competitive ratio for all metric spaces. Our algorit hm uses a recent result of Bartal [Bar96] that an arbitrary metr ic space can be probabilistically approximated by a set of metric spaces called “ k-hierarchical well-separated trees” ( kHST’s). Indeed, the…
• Computer Science, Mathematics
SODA '10
• 2010
Recently, Coté et al. [10] proposed an approach for solving the k-server problem on Hierchically Separated Trees (HSTs). In particular, they define a problem on a uniform metric, and show that if an
• Mathematics, Computer Science
ICALP
• 2010
The main technical contribution here is to extend many of these techniques to work directly on HSTs to obtain a refined guarantee for the unfair metrical task systems problem on an HST.
• Computer Science
40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039)
• 1999
We construct an online algorithm for paging that achieves an O(r+log k) competitive ratio when compared to an offline strategy that is allowed the additional ability to "rent" pages at a cost of 1/r.
• Computer Science, Mathematics
2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
• 2011
The first polylogarithmic-competitive randomized algorithm for the k-server problem on an arbitrary finite metric space is given, which improves upon the (2k-1)-competitive algorithm of Koutsoupias and Papadimitriou whenever n is sub-exponential in k.
• Computer Science, Mathematics
Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)
• 1998
This paper derandomizes the use of Bartal's algorithm and obtains the first deterministic approximation algorithms for buy-at-bulk network design and vehicle routing and a novel view of probabilistic approximation of metric spaces as a deterministic optimization problem via linear programming.
• Computer Science, Mathematics
SIAM J. Comput.
• 2000
A lower bound of $\Omega(\sqrt{\log k / \log k})$ is proved for the competitive ratio of randomized algorithms for the k-server problem against an oblivious adversary and the bound holds for arbitrary metric spaces and provides a new lower bound for the metrical task system problem as well.
• Mathematics, Computer Science
ESA
• 1998
It is shown that the randomized 2-server problem can be reduced to the deterministic (2l; l) problem, and a lower bound of 2 is proved on the competitive ratio of the (4; 2)-server problem.
It is shown that on the line and circle, the randomized version of the k-server problem is equivalent to the fractional version, and the cases for which these versions are not equivalent are classified by presenting a fractional algorithm which cannot be simulated by any randomized algorithm.
The first general decomposition theorem for the k-server problem is presented, which implies O(polylog(k)-competitive randomized algorithms for certain metric spaces consisting of a polylogarithmic number of widely separated sub-spaces, and takes a first step towards a general O- competitive algorithm.

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