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Embedding grids into hypercubes

  • Said Bettayeb
  • Zevi Miller
  • I. Hal Sudborough
Simulation And Embedding Of Parallel Networks Invited Presentation
Part of the Lecture Notes in Computer Science book series (LNCS, volume 319)

Abstract

We consider efficient simulations of mesh connected networks by hypercube machines. In particular, we consider embedding a mesh or grid G into the smallest hypercube that has at least as many points as G, called the optimal hypercube for G. In order to minimize simulation time we derive embeddings, i.e. one-to-one mappings of points in G to points in the hypercube, which minimize dilation, i.e. the maximum distance in the hypercube between images of adjacent points of G. Our results are:
  1. (1)

    There is a dilation 2 embedding of the [m×k] grid into its optimal hypercube, under conditions described in Theorem 2.1.

     
  2. (2)

    For any k<d, there is a dilation k+1 embedding of a [a1×a2× ... ×ad] grid into its optimal hypercube, under conditions described in Theorem 3.1.

     
  3. (3)

    A lower bound on dilation in embedding multi-dimensional meshes into their optimal hypercube as described in Theorem 3.2.

     

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Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Said Bettayeb
    • 1
  • Zevi Miller
    • 2
  • I. Hal Sudborough
    • 1
  1. 1.Computer Science ProgramUniversity of Texas at DallasRichardson
  2. 2.Dept. of Math and StatisticsMiami UniversityOxford

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