# 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}
}
• Published 7 October 2011
• Computer Science, Mathematics
• 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
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.
5 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
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, Mathematics
WAOA
• 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
For each fixed finite metrics, the analysis of a class of online problems that includes the $k-server problem in finite metrics such that the authors only have to consider finite sequences of request qualifies as a competitive ratio approximation scheme as defined by G\"unther et al. Randomized Online Algorithms with High Probability Guarantees • Mathematics, Computer Science STACS • 2014 A broad class of online problems is defined that includes some of the well-studied problems like paging, k-server and metrical task systems on finite metrics, and it is shown that for these problems it is possible to obtain another algorithm that achieves the same solution quality up to an arbitrarily small constant error with high probability. A Fast Algorithm for Online k-servers Problem on Trees • Computer Science ArXiv • 2020 A new time-efficient implementation of the best competitive ratio online algorithms for thek-servers problem on trees, which has$O(n)$time complexity for preprocessing and$O\left(k(\log n)^2\right)$for processing a query. Weighted k-Server Bounds via Combinatorial Dichotomies • Computer Science, Mathematics 2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS) • 2017 A doubly exponential lower bound on the competitive ratio of any deterministic online algorithm, that essentially matches the known upper bounds for the problem and closes a large and long-standing gap. Settling the Randomized k-sever Conjecture on Some Special Metrics The randomized$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, Mathematics
Theor. Comput. Sci.
• 2012
AN ONLINE ALGORITHM FOR THE 2{SERVER PROBLEM ON THE LINE WITH IMPROVED COMPETITIVENESS
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.