The Weighted 2-Server Problem
We consider a generalized 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, we prove that no memoryless randomized algorithm has a constant competitive ratio. We study a subproblem in which a request specifies two points to be covered by the servers, and the algorithm decides which server to move to which point; we give a 9-competitive deterministic algorithm for any metric space (no better ratio is possible).
KeywordsWork Function Competitive Ratio Online Algorithm Deterministic Algorithm Uniform Space
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- 1.D. Achlioptas, M. Chrobak, and J. Noga. Competitive analysis of randomized paging algorithms. In Proc. 4th European Symp. on Algorithms, volume 1136 of Lecture Notes in Computer Science, pages 419–430. Springer, 1996.Google Scholar
- 2.R. A. Baeza-Yates, J. C. Culberson, and G. J. E. Rawlins. Searching with uncertainty. In Proc. 1st Scandinavian Workshop on Algorithm Theory, Lecture Notes in Computer Science, pages 176–189. Springer, 1988.Google Scholar
- 3.Y. Bartal, A. Blum, C. Burch, and A. Tomkins. A polylog(n)-competitive algorithm for metrical task systems. In Proc. 29th Symp. Theory of Computing, pages 711–719, 1997.Google Scholar
- 4.Y. Bartal, M. Chrobak, and L. L. Larmore. A randomized algorithm for two servers on the line. In Proc. 6th European Symp. on Algorithms, Lecture Notes in Computer Science, pages 247–258. Springer, 1998.Google Scholar
- 5.Y. Bartal and E. Grove. The harmonic k-server algorithm is competitive. To appear in Journal of the ACM.Google Scholar
- 6.S. Ben-David, A. Borodin, R. M. Karp, G. Tardos, and A. Widgerson. On the power of randomization in on-line algorithms. In Proc. 22nd Symp. Theory of Computing, pages 379–386, 1990.Google Scholar
- 7.A. Blum, H. Karloff, Y. Rabani, and M. Saks. A decomposition theorem and lower bounds for randomized server problems. In Proc. 33rd Symp. Foundations of Computer Science, pages 197–207, 1992.Google Scholar
- 8.A. Borodin and R. El-Yaniv. Online Computation and Competitive Analysis. Cambridge University Press, 1998.Google Scholar
- 13.M. Chrobak and L. L. Larmore. Metrical task systems, the server problem, and the work function algorithm. In Online Algorithms: State of the Art, pages 74–94. Springer-Verlag, 1998.Google Scholar
- 16.E. Feuerstein, S. Seiden, and A. S. de Loma. The related server problem. Manuscript, 1999.Google Scholar
- 20.E. Koutsoupias and D. Taylor. Lower bounds for the CNN problem. To appear in STACS 2000 (this volume), 2000.Google Scholar