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Parallel implementations of graph embeddings

Extended abstract
  • Fred S. Annexstein
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 678)

Abstract

This paper addresses the problem of how to efficiently implement a certain class of network emulations. We provide a framework for studying and implementing graph embeddings at a fine level of abstraction, suitable for the specification of pseudocode. Our results show that many networks with regular structure, including meshes, complete-binary trees, butterflies, X-trees, and mesh-of-trees can be efficiently embedded within a hypercube using SIMD-style parallel algorithms for translating node labels.

Keywords

Tree Node Transformation Graph Gray Code Label Algorithm Standard Label 
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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References

  1. 1.
    S.N. Bhatt, F.R.K. Chung, F.T. Leighton, A.L. Rosenberg (1991): Efficient embeddings of trees in hypercubes. SIAM J. Comput., to appear.Google Scholar
  2. 2.
    T. Bräunl (1989): Structured SIMD programming in Parallaxis. Structured Programming 10/3, 121–132.Google Scholar
  3. 3.
    M.Y. Chan (1988): Dilation-2 embedding of grids into hypercubes. Intl. Conf. on Parallel Processing, 295–298.Google Scholar
  4. 4.
    M.Y. Chan and F.Y.L. Chin (1990): Parallelized simulation of grids by hypercubes. Tech. Rpt. TR-90-11, Univ. Hong Kong.Google Scholar
  5. 5.
    D.S. Greenberg (1987): Minimum expansion embeddings of meshes in hypercubes. Tech. Rpt. DCS/RR-535, Yale Univ.Google Scholar
  6. 6.
    D.S. Greenberg, L.S. Heath and A.L. Rosenberg (1990): Optimal embeddings of butterfly-like graphs in the hypercube. Math. Syst. Th. 23, 61–77.Google Scholar
  7. 7.
    I. Havel and P. Liebl (1973): Embedding the polytomic tree into the n-cube. Časopis pro Pěstování Matematiky 98, 307–314.Google Scholar
  8. 8.
    F.T. Leighton (1992): Introduction to Parallel Algorithms and Architectures. Morgan Kaufmann, San Mateo.Google Scholar
  9. 9.
    B. Monien and I.H. Sudborough (1990): Embedding one interconnection network on another. In Computational Graph Theory (G. Tinhofer et al., eds,) Springer Verlag, 257–282.Google Scholar
  10. 10.
    L. Snyder (1990): The XYZ abstraction levels of Poker-like languages. In Languages and Compilers for Parallel Computing (D. Gelernter et al., eds.) MIT Press, 470–489.Google Scholar
  11. 11.
    H.S. Wilf (1989): Combinatorial algorithms: an update, CBMS-55, SIAM.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Fred S. Annexstein
    • 1
  1. 1.Department of Computer ScienceUniversity of CincinnatiCincinnati

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