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The Average Case Analysis of Partition Sorts

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Algorithms – ESA 2004 (ESA 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3221))

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Abstract

This paper introduces a new family of in-place sorting algorithms, the partition sorts. They are appealing both for their relative simplicity and their efficient performance. They perform Θ(n log n) operations on the average, and \(\Theta(n \log^2\!n)\) operations in the worst case.

The partition sorts are related to another family of sorting algorithms discovered recently by Chen [Che02]. He showed empirically that one version ran faster, on the average, than quicksort, and that the algorithm family performed Θ(n log n) comparisons in the worst case; however no average case analysis was obtained.

This paper completes the analysis of Chen’s algorithm family. In particular, a bound of n log n +O(n) comparisons and Θ(n log n) operations is shown for the average case, and \(\Theta (n \log^2\!n)\) operations for the worst case. The average case analysis is somewhat unusual. It proceeds by showing that Chen’s sorts perform, on the average, no more comparisons than the partition sorts.

Optimised versions of the partition sort and Chen’s algorithm are very similar in performance, and both run marginally faster than an optimised quasi-best-of-nine variant of quicksort [BM93]. They both have a markedly smaller variance than the quicksorts.

This work was supported in part by NSF grant CCR0105678.

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Author information

Authors and Affiliations

  1. Computer Science Department, Courant Institute, New York University, 251 Mercer Street, New York, NY, 10012, USA

    Richard Cole & David C. Kandathil

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  1. Richard Cole
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  2. David C. Kandathil
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Editors and Affiliations

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

    Susanne Albers

  2. Department of Computer Science, King’s College, WC2R 2LS, London, UK

    Tomasz Radzik

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Cole, R., Kandathil, D.C. (2004). The Average Case Analysis of Partition Sorts. In: Albers, S., Radzik, T. (eds) Algorithms – ESA 2004. ESA 2004. Lecture Notes in Computer Science, vol 3221. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30140-0_23

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  • DOI: https://doi.org/10.1007/978-3-540-30140-0_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23025-0

  • Online ISBN: 978-3-540-30140-0

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