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
    StatePublished - 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

    Fingerprint

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

    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.

    A super-logarithmic lower bound for hypercubic sorting networks. / Plaxton, C. Greg; Suel, Torsten.

    Automata, Languages and Programming - 21st International Colloquium, ICALP 1994, Proceedings. Vol. 820 LNCS Springer Verlag, 1994. p. 618-629 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 820 LNCS).

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

    Plaxton, CG & 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, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 820 LNCS, Springer Verlag, pp. 618-629, Proceedings of the 1994 21st International Colloquium on Automata, Languages and Programming, ICALP'94, Jerusalem, Isr, 7/1/94.
    Plaxton CG, Suel T. A super-logarithmic lower bound for hypercubic sorting networks. In Automata, Languages and Programming - 21st International Colloquium, ICALP 1994, Proceedings. Vol. 820 LNCS. Springer Verlag. 1994. p. 618-629. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
    Plaxton, C. Greg ; Suel, Torsten. / A super-logarithmic lower bound for hypercubic sorting networks. Automata, Languages and Programming - 21st International Colloquium, ICALP 1994, Proceedings. Vol. 820 LNCS Springer Verlag, 1994. pp. 618-629 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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