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Further Properties of Cayley Digraphs and Their Applications to Interconnection Networks

  • Wenjun Xiao
  • Behrooz Parhami
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3959)

Abstract

In this short communication, we extend the known relationships between Cayley digraphs and their subgraphs and coset graphs with respect to subgroups and obtain some general results on homomorphism and distance between them. Intuitively, our results correspond to synthesizing alternative, more economical, interconnection networks by reducing the number of dimensions and/or link density of existing networks via mapping and pruning. We discuss applications of these results to well-known and useful interconnection networks such as hexagonal and honeycomb meshes.

Keywords

Mesh Network Cayley Graph Interconnection Network Semidirect Product Pruning Scheme 
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.
    Akers, S.B., Krishnamurthy, B.: A Group Theoretic Model for Symmetric Interconnection Networks. IEEE Trans. Computers 38, 555–566 (1989)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Annexstein, F., Baumslag, M., Rosenberg, A.L.: Group Action Graphs and Parallel Architectures. SIAM J. Computing 19, 544–569 (1990)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Biggs, N.: Algebraic Graph Theory. Cambridge University Press, Cambridge (1993)Google Scholar
  4. 4.
    Heydemann, M.: Cayley Graphs and Interconnection Networks. Graph Symmetry: Algebraic Methods and Applications, 167–224 (1997)Google Scholar
  5. 5.
    Leighton, F.T.: Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes. Morgan Kaufmann, San Francisco (1992)MATHGoogle Scholar
  6. 6.
    Nocetti, F.G., Stojmenovic, I., Zhang, J.: Addressing and Routing in Hexagonal Networks with Applications for Tracking Mobile Users and Connection Rerouting in Cellular Networks. IEEE Trans. Parallel and Distributed Systems 13, 963–971 (2002)CrossRefGoogle Scholar
  7. 7.
    Parhami, B.: Introduction to Parallel Processing: Algorithms and Architectures. Plenum (1999)Google Scholar
  8. 8.
    Parhami, B., Kwai, D.M.: A Unified Formulation of Honeycomb and Diamond Networks. IEEE Trans. Parallel and Distributed Systems 12, 74–80 (2001)CrossRefGoogle Scholar
  9. 9.
    Parhami, B., Kwai, D.M.: Incomplete k-ary n-cube and Its Derivatives. J. Parallel and Distributed Computing (to appear)Google Scholar
  10. 10.
    Stojmenovic, I.: Honeycomb Networks: Topological Properties and Communication Algorithms. IEEE Trans. Parallel and Distributed Systems 8, 1036–1042 (1997)CrossRefGoogle Scholar
  11. 11.
    Xiao, W.J., Parhami, B.: Some Mathematical Properties of Cayley Digraphs with Applications to Interconnection Network Design. International J. Computer Mathematics 82(5), 521–528 (2005)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Wenjun Xiao
    • 1
  • Behrooz Parhami
    • 2
  1. 1.Dept. of Computer ScienceSouth China University of TechnologyGuangzhouP.R. China
  2. 2.Department of Electrical and Computer EngineeringUniversity of CaliforniaSanta BarbaraUSA

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