Abstract
The first general decomposition theorem for the k-server problem is presented. Whereas all previous theorems are for the case of a finite metric with k + 1 points, the theorem given here allows an arbitrary number of points in the underlying metric space. This theorem implies O(polylog(k))-competitive randomized algorithms for certain metric spaces consisting of a polylogarithmic number of widely separated sub-spaces, and takes a first step towards a general O(polylog(k))-competitive algorithm. The only other cases for which polylogarithmic competitive randomized algorithms are known are the uniform metric space, and the weighted cache metric space with two weights.
This research was partially supported by an LSU Council on Research summer stipend and by the Research Competitiveness Subprogram of the Louisiana Board of Regents.
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References
Bartal, Y. Probabilistic approximation of metric spaces and its algorithmic applications. In Proceedings of the 37th IEEE Symposium on Foundations of Computer Science (1996), pp. 183–193.
Bartal, Y. On approximating arbitrary metrics by tree metrics. In Proceedings of the 30th ACM Symposium on Theory of Computing (1998), pp. 161–168.
Bartal, Y., Blum, A., Burch, C., AND Tomkins, A. A polylog(n)-competitive algorithm for metrical task systems. In Proceedings of the 29th ACM Symposium on Theory of Computing (1997), pp. 711–719.
Bartal, Y., Bollobas, B., AND Mendel, M. Ramsey-type theorems for metric spaces and their application for metrical task systems. Manuscript, 2001.
Bartal, Y., Chrobak, M., AND Larmore, L. L. A randomized algorithm for two servers on the line. Information and Computation 158, 1 (Apr 2000), 53–69.
Bein, W., Chrobak, M., AND Larmore, L. The 3-server problem in the plane. In Proceedings of the 7th Annual European Symposium on Algorithms (Jul 1999), pp. 301–312.
Ben-David, S., Borodin, A., Karp, R., Tardos, G., AND Wigderson, A. On the power of randomization in on-line algorithms. Algorithmica 11,1 (Jan 1994), 2–14.
Blum, A., Burch, C., AND Kalai, A. Finely-competitive paging. In Proceedings of the 40th IEEE Symposium on Foundations of Computer Science (1999), pp. 450–457.
Blum, A., Karloff, H., Rabani, Y., AND Saks, M. A decomposition theorem for task systems and bounds for randomized server problems. SIAM Journal on Computing 30,5 (Dec 2000), 1624–1661.
Borodin, A., AND El-Yaniv, R. Online Computation and Competitive Analysis. Cambridge University Press, 1998.
Borodin, A., Linial, N., AND Saks, M. An optimal online algorithm for metrical task systems. Journal of the ACM 39,4 (Oct 1992), 745–763.
Chrobak, M., Karloff, H., Payne, T., AND Vishwanathan, S. New results on server problems. SIAM Journal on Discrete Mathematics 4,2 (May 1991), 172–181.
Hrobak, M., AND Larmore, L. An optimal on-line algorithm for k-servers on trees. SIAM Journal on Computing 20, 1 (Feb 1991), 144–148.
Chrobak, M., AND Larmore, L. L. Server problems and on-line games. In Proceedings of the DIMACS Workshop on On-line Algorithms (Feb 1991), pp. 11–64.
Chrobak, M., Larmore, L. L., Llund, C., AND Reingold, N. A better lower bound on the competitive ratio of the randomized 2-server problem. Information Processing Letters 63,2 (1997), 79–83.
Fiat, A., Karp, R., Luby, M., Mgeoch, L., Sleator, D., AND Young, N. Competitive paging algorithms. Journal of Algorithms 12,4 (Dec 1991), 685–699.
Fiat, A., AND Mendel, M. Better algorithms for unfair metrical task systems and applications. In Proceedings of the 32nd Annual ACM Symposium on Theory of Computing (May 2000), pp. 725–734.
Fiat, A., AND Woeginger, G., Eds. On-Line Algorithms—The State of the Art. Lecture Notes in Computer Science. Springer-Verlag, 1998.
Irani, S. Randomized weighted caching with two page weights. Manuscript, 1999.
Karlin, A., Manasse, M., Mcgeoch, L., AND Owicki, S. Competitive randomized algorithms for nonuniform problems. Algorithmica 11,6 (Jun 1994), 542–571.
Karloff, H., Rabani, Y., AND Ravid, Y. Lower bounds for randomized k-server and motion-planning algorithms. SIAM Journal on Computing 23,2 (Apr 1994), 293–312.
Koutsoupias, E., AND Apadimitriou, C. On the k-server conjecture. Journal of the ACM 42 (1995), 971–983.
Koutsoupias, E., AND Papadimitriou, C. The 2-evader problem. Information Processing Letters 57,5 (Mar 1996), 249–252.
Manasse, M., Mcgeoch, L., AND Sleator, D. Competitive algorithms for server problems. Journal of Algorithms 11,2 (Jun 1990), 208–230.
Mcgeoch, L., AND Sleator, D. A strongly competitive randomized paging algorithm. Algorithmica 6,6 (1991), 816–825.
Seiden, S. S. Unfair problems and randomized algorithms for metrical task systems. Information and Computation 148,2 (Feb 1999), 219–240.
Sleator, D., AND Tarjan, R. Amortized efficiency of list update and paging rules. Communications of the ACM 28,2 (Feb 1985), 202–208.
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Seiden, S.S. (2001). A General Decomposition Theorem for the k-Server Problem. In: auf der Heide, F.M. (eds) Algorithms — ESA 2001. ESA 2001. Lecture Notes in Computer Science, vol 2161. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44676-1_7
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DOI: https://doi.org/10.1007/3-540-44676-1_7
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