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Algorithmica

, Volume 11, Issue 1, pp 2–14 | Cite as

On the power of randomization in on-line algorithms

  • S. Ben-David
  • A. Borodin
  • R. Karp
  • G. Tardos
  • A. Wigderson
Article

Abstract

Against in adaptive adversary, we show that the power of randomization in on-line algorithms is severely limited! We prove the existence of an efficient “simulation” of randomized on-line algorithms by deterministic ones, which is best possible in general. The proof of the upper bound is existential. We deal with the issue of computing the efficient deterministic algorithm, and show that this is possible in very general cases.

Key words

On-line algorithms Competitive analysis Randomized algorithms Game theory 

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References

  1. [1]
    P. Berman, H. J. Karloff, and G. Tardos. A competitive three-server algorithm. Proceedings of the First Annual ACM-SIAM Symposium on Discrete Algorithms, pages 280–290, Jan. 1990.Google Scholar
  2. [2]
    A. Borodin, N. Linial, and M. Saks. An optimal on-line algorithm for metrical task systems. Proceedings of the 19th Annual ACM Symposium on Theory of Computing, pages 373–382, New York City, May 1987.Google Scholar
  3. [3]
    A. Borodin, N. Linial, and M. Saks. An optimal on-line algorithm for metrical task systems.J. Assoc. Comput. Mach., 39(4):743–763, 1992.Google Scholar
  4. [4]
    M. Chrobak, H. Karloff, T. Payne, and S. Vishwanathan. New results on server problems.Proceedings of the First Annual ACM-SIAM Symposium on Discrete Algorithms, pages 291–300, Jan. 1990. To appear inSIAM J. Discrete Math. Google Scholar
  5. [5]
    D. Coppersmith, P. Doyle, P. Raghavan, and M. Snir. Random walks on weighted graphs, and applications to on-line algorithms.Proceedings of the 22nd Annual ACM Symposium on Theory of Computing, pages 369–378, Baltimore, MD, May 1990.Google Scholar
  6. [6]
    X. Deng, and S. Mahajan. Randomization vs. computability in on-line problems.Proceedings of the 23rd Annual ACM Symposium on Theory of Computing, pages 289–298, New Orleans, LA, May 1991.Google Scholar
  7. [7]
    A. Fiat, R. M. Karp, M. Luby, L. A. McGeoch, D. D. Sleator, and N. E. Young. Competitive paging algorithms.J. Algorithms, 12:685–699, 1991.Google Scholar
  8. [8]
    A. Fiat, Y. Rabani, and Y. Ravid. Competitive K-server algorithms.Proceedings of the 31st Annual IEEE Symposium on Foundations of Computer Science, pages 454–463, St. Louis, MO, Oct. 1990.Google Scholar
  9. [9]
    D. Gale and F. M. Stewart.Infinite games with perfect information. In W. H. Kuhn and A. W. Tucker, editors,Contributions to the Theory of Games, Vol. II, pages 245–266. Annals of Mathematics Studies, 28, Princeton University Press, Princeton, NJ, 1953.Google Scholar
  10. [10]
    E. Grove. The harmonick-server algorithm is competitive.Proceedings of the 23rd Annual ACM Symposium on Theory of Computing, pages 260–266, New Orleans, LA, May 1991.Google Scholar
  11. [11]
    A. R. Karlin, M. S. Manasse, L. Rudolph, and D. D. Sleator. Competitive snoopy caching.Algorithmica, 3(1):79–119, 1988.Google Scholar
  12. [12]
    M. S. Manasse, L. A. McGeoch, and D. D. Sleator. Competitive algorithms for on-line problems.J. Algorithms, 11:208–230, 1990.Google Scholar
  13. [13]
    D. A. Martin. Borel determinacy.Ann. of Math., 102:363–371, 1975.Google Scholar
  14. [14]
    L. A. McGeoch and D. D. Sleator. A strongly competitive randomized paging algorithm.Algorithmica, 6(6):816–825, 1991.Google Scholar
  15. [15]
    P. Raghavan and M. Snir. Memory vs. randomization in on-line algorithms. In ICALP, Italy, July 1989.Proceedings of the 16th ICALP, pages 687–703. LNCS, 372, Springer-Verlag, Berlin, 1990.Google Scholar
  16. [16]
    P. Raghavan and M. Snir. Memory vs. randomization in on-line algorithms. Revised version of the ICALP paper. Submitted toJ. Assoc. Comput. Mach. Google Scholar
  17. [17]
    D. D. Sleator and R. E. Tarjan. Amortized efficiency of list update and paging rules.Comm. ACM, 28(2):202–208, 1985.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1994

Authors and Affiliations

  • S. Ben-David
    • 1
  • A. Borodin
    • 2
  • R. Karp
    • 3
  • G. Tardos
    • 4
  • A. Wigderson
    • 5
  1. 1.TechnionHaifaIsrael
  2. 2.Department of Computer ScienceUniversity of TorontoTorontoCanada
  3. 3.University of California at Berkeley and International Computer Science InstituteBerkeleyUSA
  4. 4.Eötvös UniversityBudapestHungary
  5. 5.Hebrew UniversityJerusalemIsrael

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