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Average-Case Complexity of Shellsort (Preliminary Version)

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Automata, Languages and Programming

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1644))

Abstract

We prove a general lower bound on the average-case complexity of Shellsort: the average number of data-movements (and comparisons) made by a p-pass Shellsort for any incremental sequence is Ω(pn1+1/p) for every p. The proof method is an incompressibility argument based on Kolmogorov complexity. Using similar techniques, the average-case complexity of several other sorting algorithms is analyzed.

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Author information

Authors and Affiliations

  1. Dept of Computing and Software, McMaster University, Hamilton, Ontario, L8S 4K1, Canada

    Tao Jiang

  2. Dept of Computer Science, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

    Ming Li

  3. CWI, Kruislaan 413, 1098, SJ, Amsterdam, The Netherlands

    Paul Vitányi

Authors
  1. Tao Jiang
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  2. Ming Li
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  3. Paul Vitányi
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Editor information

Editors and Affiliations

  1. Institute for Computer Science, Academy of Sciences of the Czech Republic, Pod vodarenskou vezi 2, 182 07, Prague 8 - Liben, Czech Republic

    Jirí Wiedermann

  2. ILLC-WINS-University of Amsterdam, Plantage Muidergracht 24, 1018, TV, Amsterdam, The Netherlands

    Peter van Emde Boas

  3. BRICS, Department of Computer Science, University of Aarhus, Ny Munkegade, Bldg. 540, DK, 8000, Aarhus C, Denmark

    Mogens Nielsen

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© 1999 Springer-Verlag Berlin Heidelberg

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Jiang, T., Li, M., Vitányi, P. (1999). Average-Case Complexity of Shellsort (Preliminary Version) . In: Wiedermann, J., van Emde Boas, P., Nielsen, M. (eds) Automata, Languages and Programming. Lecture Notes in Computer Science, vol 1644. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48523-6_42

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  • DOI: https://doi.org/10.1007/3-540-48523-6_42

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66224-2

  • Online ISBN: 978-3-540-48523-0

  • eBook Packages: Springer Book Archive

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