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Embedding of hypercubes into grids

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Mathematical Foundations of Computer Science 1998 (MFCS 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1450))

Abstract

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.

This work was supported by the DFG-Sonderforschungsbereich 376 “Massive Parallelität: Algorithmen, Entwurfsmethoden, Anwendungen” and by the EC ESPRIT Long Term Research Project 20244 “ALCOM-IT”.

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Authors and Affiliations

  1. Department of Math. and Computer Science, University of Paderborn, D-33102, Paderborn, Germany

    S. L. Bezrukov, M. Röttger & U. -P. Schroeder

  2. Department of Math., California State University, 92407, San Bernandino, CA, USA

    J. D. Chavez

  3. Department of Math., California State University, 92521, Riverside, CA, USA

    L. H. Harper

Authors
  1. S. L. Bezrukov
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  2. J. D. Chavez
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  3. L. H. Harper
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  4. M. Röttger
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  5. U. -P. Schroeder
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Luboš Brim Jozef Gruska Jiří Zlatuška

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© 1998 Springer-Verlag Berlin Heidelberg

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Bezrukov, S.L., Chavez, J.D., Harper, L.H., Röttger, M., Schroeder, U.P. (1998). Embedding of hypercubes into grids. In: Brim, L., Gruska, J., Zlatuška, J. (eds) Mathematical Foundations of Computer Science 1998. MFCS 1998. Lecture Notes in Computer Science, vol 1450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055820

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  • DOI: https://doi.org/10.1007/BFb0055820

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64827-7

  • Online ISBN: 978-3-540-68532-6

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