Self-organizing data structures with dependent accesses
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.
KeywordsMarkov Chain Search Time Search Cost Current Block Ergodic Markov Chain
Unable to display preview. Download preview PDF.
- 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.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.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
- 6.G. H. Gonnet, and R. Baeza-Yates. Handbook of Algorithms and Data Structures. Addison-Wesley, 1991.Google Scholar
- 7.G. Hotz. Search tress and search graphs for markov sources. Journal of Information Processing and Cybernetics, 29:283–292, 1993.Google Scholar
- 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
- 10.J. G. Kemeny and J. L. Snell. Finite Markov Chains. Van Nostrand, Princeton, 1960.Google Scholar
- 11.J. H. B. Kemperman. The First Passage Problem for a Stationary Markov Chain. University Press, Chicago, 1961.Google Scholar
- 12.K. Lam. Comparison of self-organizing linear search. Journal of Applied Probability, 21:763–776, 1984.Google Scholar
- 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.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.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