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The Number of Symbol Comparisons in QuickSort and QuickSelect

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Automata, Languages and Programming (ICALP 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5555))

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Abstract

We revisit the classical QuickSort and QuickSelect algorithms, under a complexity model that fully takes into account the elementary comparisons between symbols composing the records to be processed. Our probabilistic models belong to a broad category of information sources that encompasses memoryless (i.e., independent-symbols) and Markov sources, as well as many unbounded-correlation sources. We establish that, under our conditions, the average-case complexity of QuickSort is O(nlog2 n) [rather than O(nlogn), classically], whereas that of QuickSelect remains O(n). Explicit expressions for the implied constants are provided by our combinatorial–analytic methods.

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Author information

Authors and Affiliations

  1. GREYC, CNRS and University of Caen, 14032, Caen Cedex, France

    Brigitte Vallée & Julien Clément

  2. Applied Mathematics and Statistics, The Johns Hopkins University, Baltimore, MD, 21218-2682, USA

    James Allen Fill

  3. Algorithms Project, INRIA-Rocquencourt, 78153, Le Chesnay, France

    Philippe Flajolet

Authors
  1. Brigitte Vallée
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  2. Julien Clément
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  3. James Allen Fill
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  4. Philippe Flajolet
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Freiburg, Georges Köhler Allee 79, 79110, Freiburg, Germany

    Susanne Albers

  2. Department of Computer and Systems Sciences, Sapienza University of Rome, Via Ariosto 25, 00184, Roma, Italy

    Alberto Marchetti-Spaccamela

  3. Google R&D Center, School of Computer Science, Tel Aviv University, 69978, Tel Aviv, Israel

    Yossi Matias

  4. University of Patras and CTI, N. Kazantzaki Street 1, 26504 Rion, Patras, Greece

    Sotiris Nikoletseas

  5. RWTH Aachen, Lehrstuhl Informatik 7, Ahornstraße 55, 52056, Aachen, Germany

    Wolfgang Thomas

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© 2009 Springer-Verlag Berlin Heidelberg

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Vallée, B., Clément, J., Fill, J.A., Flajolet, P. (2009). The Number of Symbol Comparisons in QuickSort and QuickSelect. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds) Automata, Languages and Programming. ICALP 2009. Lecture Notes in Computer Science, vol 5555. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02927-1_62

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  • DOI: https://doi.org/10.1007/978-3-642-02927-1_62

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02926-4

  • Online ISBN: 978-3-642-02927-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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