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Aegean Workshop on Computing

AWOC 1986: VLSI Algorithms and Architectures pp 84–95Cite as

Lower bounds for sorting on mesh-connected architectures

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 227))

Abstract

Lower bounds for sorting on mesh-connected arrays of processors are presented. For sorting N = n1n2...nr elements on an n1 × n2 × ... × nr array 2(n1 + ... + nr−1) + nr data interchange steps are needed asymptotically. For two dimensions these bounds are asymptotically best possible provided that n1 and n2 are powers of 2. In this case the generalized s2-way merge sort of Thompson and Kung turns out to be asymptotically optimal. The minimal asymptotic bound of 2√2N interchange steps can be obtained only by sorting algorithms suitable for √N/2 × √2N meshes. For r ≥ 3 dimensions an analysis of aspect-ratios also indicates that there might be mesh-connected architectures which are better suited for sorting than simple r-dimensional cubes.

This work was done at the Institut für Informatik und Praktische Mathematik, University of Kiel, West Germany.

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References

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Authors and Affiliations

  1. Institut für Informatik, Technische Universität München, Arcisstr. 21, D-8000, München 2, W. Germany

    Manfred Kunde

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  1. Manfred Kunde
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Editor information

Filia Makedon Kurt Mehlhorn T. Papatheodorou P. Spirakis

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© 1986 Springer-Verlag Berlin Heidelberg

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Kunde, M. (1986). Lower bounds for sorting on mesh-connected architectures. In: Makedon, F., Mehlhorn, K., Papatheodorou, T., Spirakis, P. (eds) VLSI Algorithms and Architectures. AWOC 1986. Lecture Notes in Computer Science, vol 227. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16766-8_8

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  • DOI: https://doi.org/10.1007/3-540-16766-8_8

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16766-2

  • Online ISBN: 978-3-540-38746-6

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