A superlogarithmic lower bound for shuffle-unshuffle sorting networks

C. G. Plaxton, T. Suel

    Research output: Contribution to journalArticle

    Abstract

    Shuffle-unshuffle sorting networks are a class of comparator networks whose structure maps efficiently to the hypercube and any of its bounded degree variants. Recently, n-input shuffle-unshuffle sorting networks with depth 2O(√lg lg n) lg n have been discovered. These networks are the only known sorting networks of depth o(lg2 n) that are not based on expanders, and their existence raises the question of whether a depth of O (lg n) can be achieved by any shuffle-unshuffle sorting network. In this paper we resolve this question by establishing an Ω (lg n lg lg n/lg lg lg n) lower bound on the depth of any n-input shuffle-unshuffle sorting network. Our lower bound can be extended to certain restricted classes of nonoblivious sorting algorithms on hypercubic machines.

    Original languageEnglish (US)
    Pages (from-to)233-254
    Number of pages22
    JournalTheory of Computing Systems
    Volume33
    Issue number3
    StatePublished - May 2000

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    Sorting Networks
    Shuffle
    Sorting
    Lower bound
    Expander
    Sorting algorithm
    Hypercube
    Network Structure
    Resolve

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Computational Theory and Mathematics
    • Mathematics(all)

    Cite this

    A superlogarithmic lower bound for shuffle-unshuffle sorting networks. / Plaxton, C. G.; Suel, T.

    In: Theory of Computing Systems, Vol. 33, No. 3, 05.2000, p. 233-254.

    Research output: Contribution to journalArticle

    Plaxton, C. G. ; Suel, T. / A superlogarithmic lower bound for shuffle-unshuffle sorting networks. In: Theory of Computing Systems. 2000 ; Vol. 33, No. 3. pp. 233-254.
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