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Annual Symposium on Theoretical Aspects of Computer Science

STACS 1987: STACS 87 pp 408–419Cite as

Optimal sorting on multi-dimensionally mesh-connected computers

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 247))

Abstract

An algorithm is presented sorting N=n1n2...nr, r≧2, elements on an n1 × n2 × ... × nr mesh-connected array of processors within 2(n1+...+nr−1)+nr+0(n1 1−ε+...+nr 1−ε), ɛ>0, data interchange steps. Hence this algorithm asymptotically matches the quite recently given lower bound for r-dimensional meshes. The asymptotically optimal lower bound of (2r/21/r) N1/r interchange steps can only be obtained on r-dimensional meshes withaspect ratio ni : nr=1 : 2 for all i=1,...,r−1. Moreover, for meshes with wraparound connections the slightly altered algorithm only need 1.5(n1+...+nr−1)+nr+0(n1 1−ε+...+nr 1−ε) data interchange steps, which asymptotically is significantly smaller than the lower bound for sorting on meshes without wrap-arounds.

This work was supported by the Siemens AG, München.

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Author information

Authors and Affiliations

  1. Institut für Informatik TU München, Arcisstr. 21, D-8000, München 2

    Manfred Kunde

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  1. Manfred Kunde
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Editor information

Franz J. Brandenburg Guy Vidal-Naquet Martin Wirsing

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© 1987 Springer-Verlag Berlin Heidelberg

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Kunde, M. (1987). Optimal sorting on multi-dimensionally mesh-connected computers. In: Brandenburg, F.J., Vidal-Naquet, G., Wirsing, M. (eds) STACS 87. STACS 1987. Lecture Notes in Computer Science, vol 247. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0039623

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  • DOI: https://doi.org/10.1007/BFb0039623

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-17219-2

  • Online ISBN: 978-3-540-47419-7

  • eBook Packages: Springer Book Archive

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