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Workshop on Algorithms and Data Structures

WADS 2015: Algorithms and Data Structures pp 189–199Cite as

Select with Groups of 3 or 4

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9214))

Abstract

We revisit the selection problem, namely that of computing the ith order statistic of n given elements, in particular the classical deterministic algorithm by grouping and partition due to Blum, Floyd, Pratt, Rivest, and Tarjan (1973). While the original algorithm uses groups of odd size at least 5 and runs in linear time, it has been perpetuated in the literature that using groups of 3 or 4 will force the worst-case running time to become superlinear, namely \(\Omega (n \log {n})\). We first point out that the arguments existent in the literature justifying the superlinear worst-case running time fall short of proving this claim. We further prove that it is possible to use group size 3 or 4 while maintaining the worst case linear running time. To this end we introduce two simple variants of the classical algorithm, the repeated step algorithm and the shifting target algorithm, both running in linear time.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Wisconsin-Milwaukee, Milwaukee, 53201-0784, USA

    Ke Chen & Adrian Dumitrescu

Authors
  1. Ke Chen
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  2. Adrian Dumitrescu
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Correspondence to Ke Chen .

Editor information

Editors and Affiliations

  1. Carleton University, Ottawa, Canada

    Frank Dehne

  2. Carleton University, Ottawa, Canada

    Jörg-Rüdiger Sack

  3. University of Victoria, Victoria, Canada

    Ulrike Stege

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© 2015 Springer International Publishing Switzerland

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Chen, K., Dumitrescu, A. (2015). Select with Groups of 3 or 4. In: Dehne, F., Sack, JR., Stege, U. (eds) Algorithms and Data Structures. WADS 2015. Lecture Notes in Computer Science(), vol 9214. Springer, Cham. https://doi.org/10.1007/978-3-319-21840-3_16

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  • DOI: https://doi.org/10.1007/978-3-319-21840-3_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21839-7

  • Online ISBN: 978-3-319-21840-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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