Routing and Wavelength Assignment for Exchanged Hypercubes in Linear Array Optical Networks

  • Yu-Liang Liu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8707)


The exchanged hypercube, denoted by EH(s, t), is a new interconnection network obtained by systematically removing links from the hypercube, while preserves many appealing properties. This paper addresses the routing and wavelength assignment for realizing exchanged hypercubes communication patterns on linear array WDM optical networks. By using congestion estimation, we derive a lower bound of the minimum number of required wavelengths, and propose an optimal wavelength assignment algorithm that uses 2 s + t − 1 + \(\lfloor\)2 t /3\(\rfloor\) wavelengths.


WDM optical networks Routing and wavelength assignment Exchanged hypercube Linear array Congestion 


  1. 1.
    Beauquier, B., Bermond, J.C., Gargano, L., Hell, P., Prennes, S., Vaccaro, U.: Graph problems arising from wavelength routing in all optical networks. In: Proceedings of the Second Workshop in Optics and Computer Science, pp. 76–84 (1997)Google Scholar
  2. 2.
    Bezrukov, S., Chavez, J., Harper, L., Rottger, M., Schroeder, U.P.: The congestion of n-cube layout on a rectangular grid. Discrete Mathematics 213(1-3), 13–19 (2000)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Chen, Y., Shen, H.: Routing and wavelength assignment for hypercube in array-based WDM optical networks. Journal of Parallel and Distributed Computing 70, 59–68 (2010)CrossRefzbMATHGoogle Scholar
  4. 4.
    Chen, Y., Shen, H., Liu, F.: Wavelength assignment for realizing parallel FFT on regular optical networks. Journal of Supercomputing 36, 3–16 (2006)CrossRefGoogle Scholar
  5. 5.
    Chen, Y., Shen, H., Zhang, H.: Wavelength assignment for directional hypercube communications on a class of WDM optical networks. In: Proceedings of International Conference on Parallel Processing, pp. 288–595 (2007)Google Scholar
  6. 6.
    Klavzar, S., Ma, M.: The domination number of exchanged hypercubes. Information Processing Letters 114, 159–162 (2014)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Li, X.J., Xu, J.M.: Generalized measures of fault tolerance in exchanged hypercubes. Information Processing Letters 113, 533–537 (2013)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Libeskind-Hadas, R., Melhem, R.G.: Multicast routing and wavelength assignment in multihop optical networks. IEEE/ACM Transactions on Networking 10(5), 621–629 (2002)CrossRefGoogle Scholar
  9. 9.
    Loh, P.K.K., Hsu, W.J., Pan, Y.: The exchanged hypercube. IEEE Transactions on Parallel and Distributed Systems 16(9), 866–874 (2005)CrossRefGoogle Scholar
  10. 10.
    Ma, M.: The connectivity of exchanged hypercubes, Discrete Mathematics. Algorithms and Applications 2(2), 51–57 (2010)Google Scholar
  11. 11.
    Ma, M., Zhu, L.: The super connectivity of exchanged hypercubes. Information Processing Letters 111, 360–364 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    Yu, C., Yang, X., Yang, L., Zhang, J.: Routing and wavelength assignment for 3-aryn-cube in array-based optical network. Information Processing Letters 112, 252–256 (2012)CrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    Yu, C., Yang, X., Yang, L., Zhang, J.: Routing and wavelength assignment for 3-ary n-cube communication patterns in linear array optical networks for n communication rounds. Information Processing Letters 113, 677–680 (2013)CrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    Yuan, X., Melhem, R.: Optimal routing and channel assignments for hypercube communi- cation on optical mesh-like processor arrays. In: Proceedings of The Fifth International Conference on Massively Parallel Processing, pp. 76–84 (1998)Google Scholar
  15. 15.
    Zang, H., Jue, J.P., Bukherjee, B.: A review of routing and wavelength assignment approaches for wavelength-routed optical networks. Optical Network Magazine 1(1), 47–60 (2000)Google Scholar
  16. 16.
    Li, Y., Peng, S., Chu, W.: Efficient collective communications in dual-cube. Journal of Supercomputing 28, 71–90 (2004)CrossRefzbMATHGoogle Scholar

Copyright information

© IFIP International Federation for Information Processing 2014

Authors and Affiliations

  • Yu-Liang Liu
    • 1
  1. 1.Department of Computer Science and Information EngineeringAletheia UniversityNew Taipei CityTaiwan

Personalised recommendations