Embedding Interconnection Networks in Crossed Cubes

  • Emad AbuelrubEmail author
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 60)


The hypercube parallel architecture is one of the most popular interconnection networks due to many of its attractive properties and its suitability for general purpose parallel processing. An attractive version of the hypercube is the crossed cube. It preserves the important properties of the hypercube and most importantly reduces the diameter by a factor of 2. In this chapter, we show the ability of the crossed cube as a versatile architecture to simulate other interconnection networks efficiently. We present new schemes to embed complete binary trees, complete quad trees, and cycles into crossed cubes.


Binary trees crossed cubes cycles embedding interconnection networks quad trees 


  1. 1.
    Abuelrub, E. Embeddings into crossed cubes. Proceedings of the World Congress on Engineering (WCE’2009),1, London (2009)Google Scholar
  2. 2.
    Abuelrub, E. The hamiltonicity of crossed cubes in the presence of faults. Eng. Lett.16(3), 453–459 (2008)Google Scholar
  3. 3.
    Barasch, L., Lakshmivarahan, S., Dhall, S.: Embedding arbitrary meshes and complete binary trees in generalized hypercubes. Proceedings of the 1st IEEE Symposium on Parallel and Distributed Processing, pp. 202–209, 1989Google Scholar
  4. 4.
    Chang, C., Sung, T., Hsu, L.: Edge congestion and topological properties of crossed cubes. IEEE Trans. Parall. Distrib. Syst.11(1), 64–80 (2006)CrossRefGoogle Scholar
  5. 5.
    Dingle, A., Sudborough, I.: Simulating binary trees and x-trees on pyramid networks. Proceedings of the 1st IEEE Symposium on Parallel and Distributed Processing, pp. 210–219 (1989)Google Scholar
  6. 6.
    Efe, K.: The crossed cube architecture for parallel computation. IEEE Trans. Parall. Distrib. Syst.3(5), 513–524 (1992)CrossRefGoogle Scholar
  7. 7.
    El-Amaway, A., Latifi, S.: Properties and performance of folded hypercubes. IEEE Trans. Parall. Distrib. Syst.2(1), 31–42 (1991)CrossRefGoogle Scholar
  8. 8.
    Fan, J., Lin, X., Jia, X.: Optimal path embedding in crossed cubes. IEEE Trans. Parall. Distrib. Syst.16(12), 1190–1200 (2005)CrossRefGoogle Scholar
  9. 9.
    Fu, J., Chen, G.: Hamiltonicity of the hierarchical cubic network. Theory Comput. Syst.35, 59–79 (2008)MathSciNetGoogle Scholar
  10. 10.
    Keh, H., Lin, J.: On fault-tolerance embedding of hamiltonian cycles, linear arrays, and rings in a flexible hypercube. Parall. Comput.26(6), 769–781 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Latifi, S., Zheng, S.: Optimal simulation of linear array and ring architectures on multiply-twisted hypercube. In: Proceedings of the 11th International IEEE Conference on Computers and Communications, 1992Google Scholar
  12. 12.
    Lee, S., Ho, H.: A 1.5 approximation algorithm for embedding hyperedges in a cycle. IEEE Trans. Parall. Distrib. Syst.16(6), 481–487 (June 2005)CrossRefGoogle Scholar
  13. 13.
    Leighton, T.: Introduction to Parallel Algorithms and Architecture: Arrays, Trees, Hypercubes. Morgan Kaufmann, San Mateo, CA (1992)zbMATHGoogle Scholar
  14. 14.
    Lin, J.: Embedding hamiltonian cycles, linear arrays, and rings in a faulty supercube. Int. J. High Speed Comput.11(3), 189–201 (2000)zbMATHCrossRefGoogle Scholar
  15. 15.
    Ma, M., Xu, J.: Panconnectivity of locally twisted cubes. Appl. Math. Lett.17(7), 674–677 (2006)MathSciNetGoogle Scholar
  16. 16.
    Markas, T., Reif, J.: Quad tree structures for image compression applications. Inform. Process. Lett.28(6), 707–722 (1992)Google Scholar
  17. 17.
    Preparata, F., Vuillemin, J.: The cube-connected cycles: a versatile network for parallel computation. Commun. ACM.24(5), 3000–3309 (1981)CrossRefMathSciNetGoogle Scholar
  18. 18.
    Topi, L., Parisi, R., Uncini, A.: Spline recurrent neural network for quad-tree video coding. Proceedings of WIRN’2002, pp. 90–98 (2002)Google Scholar
  19. 19.
    Saad, Y., Schultz, M.: Topological properties of the hypercube. IEEE Trans. Comput.37(7), 867–872 (July 1988)CrossRefGoogle Scholar
  20. 20.
    Youyao, L.: A hypercube-based scalable interconnection network for massively parallel computing. J. Comput.3(10) (October 2008)Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Department of Computer Science, Faculty of Science and ITZarqa Private UniversityZarqaJordan

Personalised recommendations