A super-logarithmic lower bound for hypercubic sorting networks

C. Greg Plaxton, Torsten Suel

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Abstract

    Hypercubic 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 hypercubic sorting networks with depth 2O(√lg lg n) lg n have been discovered. These networks are the only known sorting networks of depth o(lg2n) 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 hypercubic 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 hypercubic sorting network. Our lower bound can be extended to certain restricted classes of non-oblivious sorting algorithms on hypercubic machines.

    Original languageEnglish (US)
    Title of host publicationAutomata, Languages and Programming - 21st International Colloquium, ICALP 1994, Proceedings
    PublisherSpringer Verlag
    Pages618-629
    Number of pages12
    Volume820 LNCS
    ISBN (Print)9783540582014
    Publication statusPublished - 1994
    EventProceedings of the 1994 21st International Colloquium on Automata, Languages and Programming, ICALP'94 - Jerusalem, Isr
    Duration: Jul 1 1994Jul 1 1994

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume820 LNCS
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Other

    OtherProceedings of the 1994 21st International Colloquium on Automata, Languages and Programming, ICALP'94
    CityJerusalem, Isr
    Period7/1/947/1/94

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    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Computer Science(all)

    Cite this

    Plaxton, C. G., & Suel, T. (1994). A super-logarithmic lower bound for hypercubic sorting networks. In Automata, Languages and Programming - 21st International Colloquium, ICALP 1994, Proceedings (Vol. 820 LNCS, pp. 618-629). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 820 LNCS). Springer Verlag.