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Self-organizing data structures with dependent accesses

  • Frank Schulz
  • Elmar Schömer
Session 13: Data Structures
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1099)

Abstract

We consider self-organizing data structures in the case where the sequence of accesses can be modeled by a first order Markov chain. For the simple-k- and batched-k-move-to-front schemes, explicit formulae for the expected search costs are derived and compared. We use a new approach that employs the technique of expanding a Markov chain. This approach generalizes the results of Gonnet/Munro/Suwanda. In order to analyze arbitrary memory-free move-forward heuristics for linear lists, we restrict our attention to a special access sequence, thereby reducing the state space of the chain governing the behaviour of the data structure.

In the case of accesses with locality (inert transition behaviour), we find that the hierarchies of self-organizing data structures with respect to the expected search time are reversed, compared with independent accesses. Finally we look at self-organizing binary trees with the move-to-root rule and compare the expected search cost with the entropy of the Markov chain of accesses.

Keywords

Markov Chain Search Time Search Cost Current Block Ergodic Markov Chain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    B. Allen and I. Munro. Self-organizing binary search trees. Journal of the ACM, 25(4):526–535, 1978.CrossRefGoogle Scholar
  2. 2.
    P. J. Burville and J. F. C. Kingman. On a model for storage and search. Journal of Applied Probability, 10:697–701, 1973.Google Scholar
  3. 3.
    Ph. Chassaing. Optimality of move-to-front for self-organizing data structures with locality of references. Annals of Applied Probability, 3(4):1219–1240, 1993.Google Scholar
  4. 4.
    F. R. K. Chung, D. J. Hajela, and P. D. Seymour. Self-organizing sequential search and Hilbert's inequalities. In Proceedings of the 17th Annual ACM Symposium on Theory of Computing, pages 217–223, New York, 1985.Google Scholar
  5. 5.
    G. H. Gonnet, J. I. Munro, and H. Suwanda. Exegesis of self-organizing linear search. SIAM Journal of Computing, 10(3):613–637, 1981.CrossRefGoogle Scholar
  6. 6.
    G. H. Gonnet, and R. Baeza-Yates. Handbook of Algorithms and Data Structures. Addison-Wesley, 1991.Google Scholar
  7. 7.
    G. Hotz. Search tress and search graphs for markov sources. Journal of Information Processing and Cybernetics, 29:283–292, 1993.Google Scholar
  8. 8.
    Y. C. Kan and S. M. Ross. Optimal list order under partial memory constraints. Journal of Applied Probability, 17:1004–1015, 1980.Google Scholar
  9. 9.
    J. Keilson and A. Kester. Monotone matrices and monotone markov processes. Stochastic Processes and Applications, 5:231–241, 1977.CrossRefGoogle Scholar
  10. 10.
    J. G. Kemeny and J. L. Snell. Finite Markov Chains. Van Nostrand, Princeton, 1960.Google Scholar
  11. 11.
    J. H. B. Kemperman. The First Passage Problem for a Stationary Markov Chain. University Press, Chicago, 1961.Google Scholar
  12. 12.
    K. Lam. Comparison of self-organizing linear search. Journal of Applied Probability, 21:763–776, 1984.Google Scholar
  13. 13.
    K. Lam, M. Y. Leung, and M. K. Siu. Self-organizing files with dependent accesses. Journal of Applied Probability, 21:343–359, 1984.Google Scholar
  14. 14.
    R. I. Phelps and L. C. Thomas. On optimal performance in self-organizing paging algorithms. Journal Inf. Optimization Science, 1:80–93, 1980.Google Scholar
  15. 15.
    F. Schulz. Self-organizing data structures with dependent accesses. MSc Thesis supervised by Prof. Dr. G. Hotz, University of Saarbrücken, 1995 (in German). See http://hamster.cs.uni-sb.de/~schulz/Google Scholar
  16. 16.
    A. M. Tenenbaum and R. M. Nemes. Two spectra of self-organizing sequential search algorithms. SIAM Journal of Computing, 11:557–566, 1982.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Frank Schulz
    • 1
  • Elmar Schömer
    • 1
  1. 1.FB 14, Informatik, Lehrstuhl Prof. Dr. G. HotzUniversität des SaarlandesSaarbrückenGermany

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