A new family of randomized algorithms for list accessing

  • Theodoulos Garefalakis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1284)


Sequential lists are a frequently used data structure for implementing dictionaries. Recently, self-organizing sequential lists have been proposed for “engines” in efficient data compression algorithms. In this paper, we investigate the problem of list accessing from the perspective of competitive analysis. We establish a connection between randomized list accessing algorithms and Markov chains, and present Markov-Move-To-Front, a family of randomized algorithms. To every finite, irreducible Markov chain corresponds a member of the family. The family includes as members well known algorithms such as Move-To-Front, Random-Move-To-Front, Counter, and Random-Reset.

First we analyze Markov-Move-To-Front in the standard model, and present upper and lower bounds that depend only on two parameters of the underlying Markov chain. Then we apply the bounds to particular members of the family. The bounds that we get are at least as good as the known bounds. Furthermore, for some algorithms we obtain bounds that, to our knowledge, are new.

We also analyze Markov-Move-To-Front in the paid exchange model. In this model, the cost of an elemant transposition is always paid, and costs d. We prove upper and lower bounds that are relatively tight. Again, we apply the bounds to known algorithms such as Random-Move-To-Front and Counter. In both cases, the upper and lower bounds match as the parameter d tends to infinity.


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  1. 1.
    Albers, S.: Improved Randomized On-line Algorithms for the List Update Problem. Proceedings of the 6th Annual ACM-SIAM Symposium on Discrete Algorithms (1995) 412–419Google Scholar
  2. 2.
    Albers, S., von Stengel, B., Werchner, W.: A Combined BIT and TIMESTAMP Algorithm for the List Update Problem. TR-95-039 (1995), International Computer Science Institute, BerkeleyGoogle Scholar
  3. 3.
    Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Draft (1996)Google Scholar
  4. 4.
    Borodin, A., El-Yaniv, R.: On Randomization in Online Computation. To appear in 12th IEEE Conference on Computational Complexity (1997).Google Scholar
  5. 5.
    El-Yaniv, R.: There are Infinitely Many Competitive-Optimal Online List Accessing Algorithms. Submitted to SODA 97.Google Scholar
  6. 6.
    Irani, S.: Two Results on the List Update Problem. Information Processing Letters 38 (6) (1991) 202–208.Google Scholar
  7. 7.
    Irani, S.: Corrected Version of the SPLIT Algorithm for the List Update Problem. (1996) ICS Department, U.C. Irvine. Technical Report 96-53. Note: Corrected version of the SPLIT algorithm appearing in [6].Google Scholar
  8. 8.
    Reingold, N., Westbrook, J., Sleator, D.: Randomized Competitive Algorithms for The List Update Problem. Algorithmica 11 (1994) 15–32.Google Scholar
  9. 9.
    Sleator, D., Tarjan, R.: Amortized Efficiency of List Update and Paging Rules. Communications of the ACM 28 (2) (1985) 202–208.Google Scholar
  10. 10.
    Teia, B.: A Lower Bound for Randomized List Update Algorithms. Information Processing Letters 47 (1993) 5–9.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Theodoulos Garefalakis
    • 1
  1. 1.Department of Computer ScienceUniversity of TorontoTorontoCanada

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