Competitive algorithms for server problems
Journal of Algorithms
An optimal on-line algorithm for K-servers on trees
SIAM Journal on Computing
New results on server problems
SIAM Journal on Discrete Mathematics
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Journal of the ACM (JACM)
A combined BIT and TIMESTAMP algorithm for the list update problem
Information Processing Letters
Information Processing Letters
A polylog(n)-competitive algorithm for metrical task systems
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
A better lower bound on the competitive ratio of the randomized 2-server problem
Information Processing Letters
Linear programs for randomized on-line algorithms
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Competitive randomized algorithms for non-uniform problems
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Randomized Algorithms for Metrical Task Systems
WADS '95 Proceedings of the 4th International Workshop on Algorithms and Data Structures
Competive Analysis of Randomized Paging Algorithms
ESA '96 Proceedings of the Fourth Annual European Symposium on Algorithms
A decomposition theorem and bounds for randomized server problems
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
Randomized Competitive Analysis for Two-Server Problems
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
A randomized algorithm for two servers in cross polytope spaces
Theoretical Computer Science
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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 first algorithm for 2 servers with competitive ratio smaller than 2 in a non-uniform metric space 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 unbiased 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.