International Workshop on Combinatorial Algorithms

IWOCA 2014: Combinatorial Algorithms pp 298-306 | Cite as

Embedding Circulant Networks into Butterfly and Benes Networks

  • R. Sundara RajanEmail author
  • Indra Rajasingh
  • Paul Manuel
  • T. M. Rajalaxmi
  • N. Parthiban
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8986)


The dilation of an embedding is defined as the maximum distance between pairs of vertices of host graph that are images of adjacent vertices of guest graph. An embedding with a long dilation faces many problems, such as long communication delay, coupling problems and the existence of different types of uncontrolled noise. In this paper, we compute the minimum dilation of embedding circulant networks into butterfly and benes networks.


Embedding Dilation Circulant network Butterfly and benes networks 



The authors would like to thank the anonymous referees for their comments and suggestions. These comments and suggestions were very helpful for improving the quality of this paper.


  1. 1.
    Chaudhary, V., Aggarwal, J.K.: Generalized mapping of parallel algorithms onto parallel architectures. In: Proceeding of International Conference on Parallel Processing, pp. 137–141 (1990)Google Scholar
  2. 2.
    Dvor̂ák, T.: Dense sets and embedding binary trees into hypercubes. Discrete Appl. Math. 155(4), 506–514 (2007)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Bezrukov, S.L., Chavez, J.D., Harper, L.H., Röttger, M., Schroeder, U.P.: Embedding of hypercubes into grids. In: Mortar Fire Control System, pp.693–701 (1998)Google Scholar
  4. 4.
    Rajasingh, I., Rajan, B., Rajan, R.S.: Embedding of special classes of circulant networks, hypercubes and generalized Petersen graphs. Int. J. Comput. Math. 89(15), 1970–1978 (2012)zbMATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    Gupta, A.K., Nelson, D., Wang, H.: Efficient embeddings of ternary trees into hypercubes. J. Parallel Distrib. Comput. 63(6), 619–629 (2003)zbMATHCrossRefGoogle Scholar
  6. 6.
    Bezrukov, S.L.: Embedding complete trees into the hypercube. Discrete Appl. Math. 110(2–3), 101–119 (2001)zbMATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    Manuel, P., Rajasingh, I., Rajan, R.S.: Embedding variants of hypercubes with dilation 2. J. Interconnect. Netw. 13(1–2), 1–16 (2012)Google Scholar
  8. 8.
    Ramanathan, P., Shin, K.G.: Reliable broadcast in hypercube multicomputers. IEEE Trans. Comput. 37(12), 1654–1657 (1988)CrossRefGoogle Scholar
  9. 9.
    Wong, G.K., Coppersmith, D.A.: A combinatorial problem related to multimodule memory organization. J. Assoc. Comput. Mach. 21(3), 392–401 (1994)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Boesch, F.T., Wang, J.: Reliable circulant networks with minimum transmission delay. IEEE Trans. Circuit Syst. 32(12), 1286–1291 (1985)zbMATHMathSciNetCrossRefGoogle Scholar
  11. 11.
    Bermond, J.C., Comellas, F., Hsu, D.F.: Distributed loop computer networks: a survey. Surv. J. Parallel Distrib. Comput. 24(1), 2–10 (1995)CrossRefGoogle Scholar
  12. 12.
    Beivide, R., Herrada, E., Balcazar, J.L., Arruabarrena, A.: Optimal distance networks of low degree for parallel computers. IEEE Trans. Comput. 40(10), 1109–1124 (1991)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Wilkov, R.S.: Analysis and design of reliable computer networks. IEEE Trans. Commun. 20(3), 660–678 (1972)CrossRefGoogle Scholar
  14. 14.
    Xu, J.M.: Topological Structure and Analysis of Interconnection Networks. Kluwer Academic Publishers, Dordrecht (2001)zbMATHCrossRefGoogle Scholar
  15. 15.
    Manuel, P., Abd-El-Barra, M.I., Rajasingh, I., Rajan, B.: An efficient representation of benes networks and its applications. J. Discrete Algorithms 6(1), 11–19 (2008)zbMATHMathSciNetCrossRefGoogle Scholar
  16. 16.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, San Francisco (1979)zbMATHGoogle Scholar
  17. 17.
    Harper, L.H.: Global Methods for Combinatorial Isoperimetric Problems. Cambridge University Press, Cambridge (2004)zbMATHCrossRefGoogle Scholar
  18. 18.
    Rajan, R.S., Miller, M., Rajasingh, I., Manuel, P.: Embedding circulant networks into certain trees. J. Comb. Optim. (submitted)Google Scholar
  19. 19.
    Rajan, R.S., Manuel, P., Rajasingh, I., Parthiban, N., Miller, M.: A lower bound for dilation of an embedding. Comput. J. (2015).

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • R. Sundara Rajan
    • 1
    Email author
  • Indra Rajasingh
    • 1
  • Paul Manuel
    • 2
  • T. M. Rajalaxmi
    • 3
  • N. Parthiban
    • 4
  1. 1.School of Advanced SciencesVIT UniversityChennaiIndia
  2. 2.Department of Information ScienceKuwait UniversitySafatKuwait
  3. 3.Department of MathematicsSSN College of EngineeringChennaiIndia
  4. 4.School of Computing Sciences and EngineeringVIT UniversityChennaiIndia

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