# A Polylogarithmic-Competitive Algorithm for the k-Server Problem

@article{Bansal2011APA, title={A Polylogarithmic-Competitive Algorithm for the k-Server Problem}, author={Nikhil Bansal and Niv Buchbinder and Aleksander Madry and Joseph Naor}, journal={2011 IEEE 52nd Annual Symposium on Foundations of Computer Science}, year={2011}, pages={267-276} }

We give the first polylogarithmic-competitive randomized algorithm for the k-server problem on an arbitrary finite metric space. In particular, our algorithm achieves a competitive ratio of Õ(log3 n log2 k) for any metric space on n points. This improves upon the (2k-1)-competitive algorithm of Koutsoupias and Papadimitriou (J. ACM 1995) whenever n is sub-exponential in k.

## 100 Citations

Polylogarithmic Competitive Ratios for the Randomized Online k-server Problem

- Mathematics
- 2013

In this paper, we will study recent work on and progress towards polylogarithmic competitive ratios for the k-server problem. For a long time, the best known competitive ratio that held for general…

An O(log k log^2 n)-competitive Randomized Algorithm for the k-Sever Problem

- Computer Science, MathematicsArXiv
- 2015

In this paper, we show that there is an O(log k log^2 n)-competitive randomized algorithm for the k-sever problem on any metric space with n points, which improved the previous best competitive ratio…

Memoryless Algorithms for the Generalized k-server Problem on Uniform Metrics

- Computer Science, MathematicsWAOA
- 2020

It is shown that the Harmonic Algorithm achieves this competitive ratio and provides matching lower bounds, which improves the doubly-exponential bound of Chiplunkar and Vishwanathan for the more general setting of uniform metrics with different weights.

A Competitive Ratio Approximation Scheme for the k-Server Problem in Fixed Finite Metrics

- Mathematics, Computer ScienceArXiv
- 2013

For each fixed finite metrics, the analysis of a class of online problems that includes the $k-server problem in finite metrics such that the authors only have to consider finite sequences of request qualifies as a competitive ratio approximation scheme as defined by G\"unther et al.

Randomized Online Algorithms with High Probability Guarantees

- Mathematics, Computer ScienceSTACS
- 2014

A broad class of online problems is defined that includes some of the well-studied problems like paging, k-server and metrical task systems on finite metrics, and it is shown that for these problems it is possible to obtain another algorithm that achieves the same solution quality up to an arbitrarily small constant error with high probability.

Weighted k-Server Bounds via Combinatorial Dichotomies

- Computer Science, Mathematics2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS)
- 2017

A doubly exponential lower bound on the competitive ratio of any deterministic online algorithm, that essentially matches the known upper bounds for the problem and closes a large and long-standing gap.

R-LINE: A better randomized 2-server algorithm on the line

- Mathematics, Computer ScienceTheor. Comput. Sci.
- 2015

Settling the Randomized k-sever Conjecture on Some Special Metrics

- Mathematics, Computer ScienceArXiv
- 2014

The randomized $k-sever conjecture is settled for the following metric spaces: line, circle, Hierarchically well-separated tree (HST), and it is shown that there is an O(\log k)-competitive randomized k-sever algorithm for above metric spaces.

R-LINE: A Better Randomized 2-Server Algorithm on the Line

- Computer Science, MathematicsWAOA
- 2012

A randomized on-line algorithm is given for the 2-server problem on the line, with competitiveness less than 1.901 against the oblivious adversary. This improves the previously best known…

AN ONLINE ALGORITHM FOR THE 2{SERVER PROBLEM ON THE LINE WITH IMPROVED COMPETITIVENESS

- Mathematics, Computer Science
- 2013

This algorithm achieves the lowest competitive ratio of any known randomized algorithm for the 2-server problem on the line, named R–LINE (for Randomized Line), by utilizing ideas from T-theory, game theory, and linear programming.

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