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Optimal embedding of a toroidal array in a linear array

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Fundamentals of Computation Theory (FCT 1991)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 529))

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Abstract

We prove that any embedding of m×n toroidal array into mn×1 linear array contains a wire of length 2min{m,n} − 2. We describe an embedding with the maximal wire length 2min{m,n} and improve this to 2n − 1 for m=n.

The second and third authors were supported by a research grant from Humboldt Foundation, Bonn, Germany

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Author information

Authors and Affiliations

  1. Department of Electrical Engineering and Computer Science, University of Newcastle, 2308, NSW, Australia

    Heiko Schröder

  2. Computing Centre, Slovak Academy of Sciences, Dúbravská 9, 84235, Bratislava, Czecho-Slovakia

    Ondrej Sýkora & Imrich Vrťo

Authors
  1. Heiko Schröder
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  2. Ondrej Sýkora
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  3. Imrich Vrťo
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Editor information

L. Budach

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© 1991 Springer-Verlag Berlin Heidelberg

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Schröder, H., Sýkora, O., Vrťo, I. (1991). Optimal embedding of a toroidal array in a linear array. In: Budach, L. (eds) Fundamentals of Computation Theory. FCT 1991. Lecture Notes in Computer Science, vol 529. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54458-5_83

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  • DOI: https://doi.org/10.1007/3-540-54458-5_83

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54458-6

  • Online ISBN: 978-3-540-38391-8

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