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
Journal of the ACM (JACM)
A better lower bound on the competitive ratio of the randomized 2-server problem
Information Processing Letters
Online computation and competitive analysis
Online computation and competitive analysis
Linear programs for randomized on-line algorithms
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Competitive analysis of randomized paging algorithms
Theoretical Computer Science
Beyond competitive analysis [on-line algorithms]
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Randomized Competitive Analysis for Two-Server Problems
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
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It has been a long-standing open problem to determine the exact randomized competitiveness of the 2-server problem, that is, the minimum competitiveness of any randomized online algorithm for the 2- server problem. For deterministic algorithms the best competitive ratio that can be obtained is 2 and no randomized algorithm is known that improves this ratio for general spaces. For the line, Bartal et al. [2] give a 155/78 competitive algorithm, but their algorithm is specific to the geometry of the line. We consider here the 2-server problem over Cross Polytope Spaces M2,4. We obtain an algorithm with competitive ratio of 19/12, and show that this ratio is best possible. This algorithm gives the second non-trivial example of metric spaces with better than 2 competitive ratio. The algorithm uses a design technique called the knowledge state technique - a method not specific to M2,4.