On fast algorithms for two servers

doi:10.1016/0196-6774(91)90035-W

Journal of Algorithms

Volume 12, Issue 4, December 1991, Pages 607-614

https://doi.org/10.1016/0196-6774(91)90035-W Get rights and content

Abstract

We consider 2-server algorithms with time complexity O(1) per each request. We show that the previously known algorithm BALANCE2 has competitiveness constant not better than 6, and we present another algorithm whose competitiveness constant is 4.

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The $k$ -server problem is perhaps the most influential online problem: natural, crisp, with a surprising technical depth that manifests the richness of competitive analysis. The $k$ -server conjecture, which was posed more than two decades ago when the problem was first studied within the competitive analysis framework, is still open and has been a major driving force for the development of the area online algorithms. This article surveys some major results for the $k$ -server problem.
The weighted 2-server problem
2004, Theoretical Computer Science
We consider a generalization of the 2-server problem in which servers have different costs. We prove that, in uniform spaces, a version of the work function algorithm is 5-competitive, and that no better ratio is possible. We also give a 5-competitive randomized, memoryless algorithm for uniform spaces, and a matching lower bound.
For arbitrary metric spaces, in contrast with the non-weighted case, we prove that there is no memoryless randomized algorithm with finite competitive ratio. We also propose a version of the problem in which a request specifies two points to be covered by the servers, and the algorithm must decide which server to move to which point. For this version, we show a 9-competitive algorithm and we prove that no better ratio is possible.
Trackless online algorithms for the server problem
2000, Information Processing Letters
A class of “simple” online algorithms for the $k$ -server problem is identified. This class, for which the term trackless is introduced, includes many known server algorithms. The $k$ -server conjecture fails for trackless algorithms. A lower bound of $23/11$ on the competitiveness of any deterministic trackless $2$ -server algorithm and a lower bound of $1+ 2 /2$ on the competitiveness of any randomized trackless $2$ -server problem are given.
The Distributed k-Server Problem - A Competitive Distributed Translator for k-Server Algorithms
1997, Journal of Algorithms
We consider thek-server problem23in a distributed setting. Given a network ofnprocessors andkidentical mobile servers, requests for service appear at the processors and a server must reach the request point. In addition to modeling problems in computer networks wherekidentical mobile resources are shared by the processors of the network, this models a realistic situation where the transfer of information is costly and there is no central control that governs the behavior of servers that move around to satisfy requests for service. We give a general translator to transform any deterministic global-control competitivek-server algorithm into a distributed competitive one. As consequences we get poly(k)-competitive distributed algorithms for the line, trees, and the ring. In contrast to the global-control case where there arek-server algorithms with competitive ratio that depends solely onk, we have a lower bound of Ω(max{k, (1/D) ·(log n/log log n)}) on the competitive ratio of any distributedk-server algorithm, where 1/Dis the ratio between the cost to transmit a message and the cost to move a server over the same distance. We also give a distributed version of the Harmonic randomizedk-server algorithm.

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On fast algorithms for two servers

Abstract

A competitive algorithm for three servers

New results on server problems