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STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
On the Competitive Ratio of the Work Function Algorithm for the k-Server Problem
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
Analysis of the Harmonic Algorithm for Three Servers
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
A Decentralized Algorithm for Coordinating Independent Peers: An Initial Examination
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ESA '98 Proceedings of the 6th Annual European Symposium on Algorithms
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On List Update and Work Function Algorithms
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Information Processing Letters
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SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
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We prove that the work function algorithm for the k-server problem has a competitive ratio at most 2k−1. Manasse et al. [1988] conjectured that the competitive ratio for the k-server problem is exactly k (it is trivially at least k); previously the best-known upper bound was exponential in k. Our proof involves three crucial ingredients: A quasiconvexity property of work functions, a duality lemma that uses quasiconvexity to characterize the configuration that achieve maximum increase of the work function, and a potential function that exploits the duality lemma.