Beyond the worst-case bisection bound

Fast sorting and ranking on meshes

Michael Kaufmann, Jop F. Sibeyn, Torsten Suel

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

    Abstract

    Sorting is an important subroutine in many parallel algorithms and has been studied extensively on meshes and related networks. If every processor of an n × n mesh is the source and destination of at most k elements, then sorting requires at least k k; n/2 steps in the worst-case, and simple algorithms have recently been proposed that nearly match this bound. However, this lower bound does not extend to non-worst-case inputs, or weaker definitions of sorting that are sufficient in many applications. In this paper, we give algorithms and lower bounds for several such problems. We first present a very simple scheme for k-k routing that performs optimally under both average-case and worst-case inputs. As an application of this scheme, we describe a simple k-k sorting algorithm based on sample sort that nearly matches this bound. The main part of the paper considers several 'sorting-like' problems. In the ranking problem, the ranks of all elements have to be determined, but there is no requirement about their final positions. We describe an algorithm running in time (1 +o(l)) k n/4 steps, which is nearly optimal under the considered model of the mesh. We show that integer versions of the sorting and ranking problems, where keys are drawn from {0,…, m — 1}, can be solved asymptotically faster than the general problems for small values of m. A related problem, the excess counting problem, can be solved in O(n) steps in many interesting cases.

    Original languageEnglish (US)
    Title of host publicationAlgorithms - ESA 1995 - 3rd Annual European Symposium, Proceedings
    PublisherSpringer Verlag
    Pages75-88
    Number of pages14
    Volume979
    ISBN (Print)3540603131, 9783540603139
    StatePublished - 1995
    Event3rd Annual European Symposium on Algorithms, ESA 1995 - Corfu, Greece
    Duration: Sep 25 1995Sep 27 1995

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume979
    ISSN (Print)03029743
    ISSN (Electronic)16113349

    Other

    Other3rd Annual European Symposium on Algorithms, ESA 1995
    CountryGreece
    CityCorfu
    Period9/25/959/27/95

    Fingerprint

    Bisection
    Sorting
    Ranking
    Mesh
    Lower bound
    Counting Problems
    Sorting algorithm
    Subroutines
    Parallel algorithms
    Parallel Algorithms
    Sort
    Excess
    Routing
    Sufficient
    Integer
    Requirements

    ASJC Scopus subject areas

    • Computer Science(all)
    • Theoretical Computer Science

    Cite this

    Kaufmann, M., Sibeyn, J. F., & Suel, T. (1995). Beyond the worst-case bisection bound: Fast sorting and ranking on meshes. In Algorithms - ESA 1995 - 3rd Annual European Symposium, Proceedings (Vol. 979, pp. 75-88). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 979). Springer Verlag.

    Beyond the worst-case bisection bound : Fast sorting and ranking on meshes. / Kaufmann, Michael; Sibeyn, Jop F.; Suel, Torsten.

    Algorithms - ESA 1995 - 3rd Annual European Symposium, Proceedings. Vol. 979 Springer Verlag, 1995. p. 75-88 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 979).

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

    Kaufmann, M, Sibeyn, JF & Suel, T 1995, Beyond the worst-case bisection bound: Fast sorting and ranking on meshes. in Algorithms - ESA 1995 - 3rd Annual European Symposium, Proceedings. vol. 979, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 979, Springer Verlag, pp. 75-88, 3rd Annual European Symposium on Algorithms, ESA 1995, Corfu, Greece, 9/25/95.
    Kaufmann M, Sibeyn JF, Suel T. Beyond the worst-case bisection bound: Fast sorting and ranking on meshes. In Algorithms - ESA 1995 - 3rd Annual European Symposium, Proceedings. Vol. 979. Springer Verlag. 1995. p. 75-88. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
    Kaufmann, Michael ; Sibeyn, Jop F. ; Suel, Torsten. / Beyond the worst-case bisection bound : Fast sorting and ranking on meshes. Algorithms - ESA 1995 - 3rd Annual European Symposium, Proceedings. Vol. 979 Springer Verlag, 1995. pp. 75-88 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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