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Efficient Embeddings of Grids into Grids

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Graph-Theoretic Concepts in Computer Science (WG 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1517))

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Abstract

In this paper we explore one-to-one embeddings of 2-dimensional grids into their ideal 2-dimensional grids. The presented results are optimal or considerably close to the optimum.

For embedding grids into grids of smaller aspect ratio, we prove a new lower bound on the dilation matching a known upper bound. The edge-congestion provided by our matrix-based construction differs from the here presented tight lower bound by at most one. For embedding grids into grids of larger aspect ratio, we establish five as an upper bound on the dilation and four as an upper bound on the edge-congestion, which are improvements of previous results.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Paderborn, Fürstenallee 11, D-33102, Paderborn, Germany

    Markus Röttger & Ulf-Peter Schroeder

Authors
  1. Markus Röttger
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  2. Ulf-Peter Schroeder
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Editor information

Editors and Affiliations

  1. Department of Computer Science, ETH Zurich, ETH Zentrum, CH-8022, Zurich, Switzerland

    Juraj Hromkovič

  2. Department of Computer Science, University of Loughborough, Loughborough, UK

    Ondrej Sýkora

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© 1998 Springer-Verlag Berlin Heidelberg

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Röttger, M., Schroeder, UP. (1998). Efficient Embeddings of Grids into Grids. In: Hromkovič, J., Sýkora, O. (eds) Graph-Theoretic Concepts in Computer Science. WG 1998. Lecture Notes in Computer Science, vol 1517. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10692760_21

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  • DOI: https://doi.org/10.1007/10692760_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65195-6

  • Online ISBN: 978-3-540-49494-2

  • eBook Packages: Springer Book Archive

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