Embedding of hypercubes into grids

  • S. L. Bezrukov
  • J. D. Chavez
  • L. H. Harper
  • M. Röttger
  • U. -P. Schroeder
Contributed Papers Trees and Embeddings
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1450)


We consider one-to-one embeddings of the n-dimensional hypercube into grids with 2n vertices and present lower and upper bounds and asymptotic estimates for minimal dilation, edge-congestion, and their mean values. We also introduce and study two new cost-measures for these embeddings, namely the sum over i=1, ..., n of dilations and the sum of edge-congestions caused by the hypercube edges of the ith dimension. It is shown that, in the simulation via the embedding approach, such measures are much more suitable for evaluating the slowdown of uniaxial hypercube algorithms then the traditional cost measures.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • S. L. Bezrukov
    • 1
  • J. D. Chavez
    • 2
  • L. H. Harper
    • 3
  • M. Röttger
    • 1
  • U. -P. Schroeder
    • 1
  1. 1.Department of Math. and Computer ScienceUniversity of PaderbornPaderbornGermany
  2. 2.Department of Math.California State UniversitySan BernandinoUSA
  3. 3.Department of Math.California State UniversityRiversideUSA

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