A randomized algorithm for two servers on the line

Yair Bartal, Marek Chrobak, Lawrence L. Larmore

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

10 Scopus citations


In the k-server problem we wish to minimize, in an online fashion, the movement cost of k servers in response to a sequence of requests. For 2 servers, it is known that the optimal deterministic algorithm has competitive ratio 2, and it has been a long-standing open problem whether it is possible to improve this ratio using randomization. We give a positive answer to this problem when the underlying metric space is a real line, by providing a randomized online algorithm for this case with competitive ratio at most 155 78 ≈ 1:987. This is the rst algorithm for 2 servers with competitive ratio smaller than 2 in a non-uniform metricspace with more than three points. We consider a more general problem called the (k; l)-server problem, in which a request is served using l out of k available servers. We show that the randomized 2-server problem can be reduced to the deterministic (2l; l)-server problem. We prove a lower bound of 2 on the competitive ratio of the (4; 2)-server problem. This implies that one unbiase random bit is not sufficient to improve the ratio of 2 for the 2-server problem. Then we give a 155 78 competitive algorithm for the (6; 3)-server problem on the real line. Our algorithm is simple and memoryless. The solution has been obtained using linear programming techniques that may have applications for other online problems.

Original languageAmerican English
Title of host publicationAlgorithms, ESA 1998 - 6th Annual European Symposium, Proceedings
PublisherSpringer Verlag
Number of pages12
ISBN (Print)3540648488, 9783540648482
StatePublished - 1998
Externally publishedYes
Event6th Annual European Symposium on Algorithms, ESA 1998 - Venice, Italy
Duration: 24 Aug 199826 Aug 1998

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1461 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference6th Annual European Symposium on Algorithms, ESA 1998

Bibliographical note

Funding Information:
1This research was partially conducted while the author was at International Computer Science Institute, University of California, Berkeley. 2Research supported by NSF Grant CCR-9503498. This research was partially conducted when the author was visiting International Computer Science Institute, University of California, Berkeley. 3Research supported by NSF Grant CCR-9503441.


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