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Data structures maxima

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 529))

Abstract

The purpose of this paper is to analyse the maxima properties (value and position) of some data structures. Our theorems concern the distribution of the random variables. Previously known results usually dealt with the mean and sometimes the variance of these random variables. Many of our results rely on diffusion techniques. That is a very powerful tool, which has already been used with some success in the analysis of algorithms.

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References

  1. Berman, S.M.Sojourns and Extremes of Stationary Processes; The Annals of Probability, 1982, 10(1), 1–46

    Google Scholar 

  2. Cohen, J.W.The Single Server Queue, Revised Edition, 1982, North-Holland

    Google Scholar 

  3. Daniels, H.E. and Skyrme, T.H.R.The Maximum of a Random Walk whose Mean Path has a Maximum; Adv. Appl. Prob., 1985, 17, 85–99

    Google Scholar 

  4. Daniels, H.E.The Maximum of a Gaussian Process whose mean Path has a Maximum, with an Application to the Strength of Bundles of Fibres; Adv. Appl. Prob., 1989, 21, 315–333

    Google Scholar 

  5. Durbin, J.The First-Passage Density of a Continuous Gaussian Process to a General Boundary; J. Appl. Prob., 1985, 22, 99–122

    Google Scholar 

  6. Flajolet, P. and Prodinger, H.Register Allocation for Unary-Binary Trees, SIAM J. on Computing, 1986, 15(3), 629–640

    Google Scholar 

  7. Flajolet, P. and Steyaert, J.M.A Branching Process Arising in Dynamic Hashing, Trie Searching and Polynomial Factorization; 9th Int. Coll., Aut. Lang. Prog. Aarhus, 1982. Lecture notes in Comp. Sc. 140, 239–251

    Google Scholar 

  8. Flajolet, P., Françon, and Vuillemin, J.Sequence of operations analysis for dynamic data structures, Journal of Algorithms, 1980, 1(2), 111–141

    Google Scholar 

  9. Flajolet, P.Approximate Counting: a Detailed Analysis; BIT, 1985, 25, 113–134

    Google Scholar 

  10. Flajolet, P., Puech, C. and Vuillemin, J.The Analysis of Simple List Structures, Inform. Sci., 1986, 38, 121–146

    Google Scholar 

  11. Iglehart, D.L.Limiting Diffusion Approximations for the Many Server Queue and the Repairman Problem; J. Appl. Prob., 1965, 2, 429–441

    Google Scholar 

  12. Iglehart, D.L.Weak Convergence of Compound Stochastic Process, I; Stoch. Proc. and their Appl., 1973, 1, 11–31

    Google Scholar 

  13. Kenyon, C. and Vitter, J.S.General Methods for the analysis of the maximum size of dynamic data structures, Proc. of the 16th ICALP, Stresa, Italy, 1989

    Google Scholar 

  14. Louchard, G.Brownian Motion and Algorithm Complexity; BIT, 1986, 26, 17–34

    Google Scholar 

  15. Louchard, G.Exact and Asymptotic Distributions in Digital and Binary Search Trees; Theor. Inf. and Appl., 1987, 21, 479–496

    Google Scholar 

  16. Louchard, G.Random Walks, Gaussian Processes and List Structures; Theor. Comp. Sc., 1987, 53, 99–124

    Google Scholar 

  17. Louchard, G., Schott, R. and Randrianarimanana, B. Dynamic Algorithms in D.E. Knuth's Model: a Probabilistic Analysis; to appear in Theor. Comp. Sc.

    Google Scholar 

  18. Louchard, G.Large Finite Population Queueing Systems. Part I: the Infinite Server Model; Commun. Statist.-Stoch. Models, 1988, 4(3), 473–505

    Google Scholar 

  19. Louchard, G., Kenyon, C. and Schott, R. Data Structures Maxima; Lab. Inf. Théorique, ULB, TR.216 and INRIA, TR.1394, January, 1991

    Google Scholar 

  20. Morrison, J., Shepp, L.A. and Van Wyk, C.J.A queueing analysis of hashing with lazy deletion, SIAM J. on Computing, 16(6), 1987.

    Google Scholar 

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L. Budach

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© 1991 Springer-Verlag Berlin Heidelberg

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Louchard, G., Kenyon, C., Schott, R. (1991). Data structures maxima. In: Budach, L. (eds) Fundamentals of Computation Theory. FCT 1991. Lecture Notes in Computer Science, vol 529. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54458-5_78

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  • DOI: https://doi.org/10.1007/3-540-54458-5_78

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54458-6

  • Online ISBN: 978-3-540-38391-8

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