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Efficient Embeddings of Grids into Grids

(Extended Abstract)
  • Markus Röttger
  • Ulf-Peter Schroeder
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1517)

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.

Keywords

Aspect Ratio Large Aspect Ratio Rightmost Column Small Aspect Ratio Isoperimetric Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Markus Röttger
    • 1
  • Ulf-Peter Schroeder
    • 1
  1. 1.Department of Computer ScienceUniversity of PaderbornPaderbornGermany

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