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Athens Conference on Applied Probability and Time Series Analysis pp 18–33Cite as

Analysis of recursive algorithms by the contraction method

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Part of the book series: Lecture Notes in Statistics ((LNS,volume 114))

Abstract

Several examples of the asymptotic analysis of recursive algorithms are investigated by the contraction method. The examples concern random permutations and binary search trees. In these examples it is demonstrated that the contraction method can be applied successfully to problems with contraction constants converging to one and with nonregular normalizations as logarithmic normalizations, which are typical in search type algorithms. An advantage of this approach is its generality and the possibility to obtain quantitative approximation results.

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References

  1. R.N. Bhattacharya and R. Ranga Rao. Normal approximation and asymptotic expansions. Wiley, 1976

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  2. M. Cramer. Stochastische Analyse rekursiver Algorithmen mit idealen Metriken. Dissertation Universität Freiburg 1995

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  4. H.M. Mahmoud. Evolution of random search trees. Wiley, 1992

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  5. S.T. Rachev. Probability metrics and the stability of stochastic models. Wiley, 1991.

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  6. S.T. Rachev and L. Rüschendorf. Probability metrics and recursive algorithms (1991). To appear in Advances in Applied Probability

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Author information

Authors and Affiliations

  1. Institut für Mathematische Stochastik, University of Freiburg, Hebelstr. 27, Freiburg, 79104, Germany

    M. Cramer & L. Rüschendorf

Authors
  1. M. Cramer
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  2. L. Rüschendorf
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Editor information

Editors and Affiliations

  1. Stochastic Analysis Program, SMS, Australian National University, Canberra, ACT, 0200, Australia

    C. C. Heyde

  2. Academy of Sciences, Mathematical Institute, Vavilov Street 42, Moscow, 333, Russia

    Yu V. Prohorov

  3. Department of Mathematics, University of Washington, Seattle, WA, 98195, USA

    Ronald Pyke

  4. Department of Statistics and Applied Probability, University of California, Santa Barbara, Santa Barbara, CA, 93106, USA

    S. T. Rachev

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© 1996 Springer Science+Business Media New York

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Cramer, M., Rüschendorf, L. (1996). Analysis of recursive algorithms by the contraction method. In: Heyde, C.C., Prohorov, Y.V., Pyke, R., Rachev, S.T. (eds) Athens Conference on Applied Probability and Time Series Analysis. Lecture Notes in Statistics, vol 114. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0749-8_2

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  • DOI: https://doi.org/10.1007/978-1-4612-0749-8_2

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-94788-4

  • Online ISBN: 978-1-4612-0749-8

  • eBook Packages: Springer Book Archive

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