Skip to main content

Hypercube Communications on Optical Chordal Ring Networks with Chord Length of Three

  • Conference paper
Advances in Computer Systems Architecture (ACSAC 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4186))

Included in the following conference series:

  • 679 Accesses

Abstract

In this paper, we study routing and wavelength assignment for realizing hypercube communications on optical WDM chordal ring networks with chord length of 3. Specifically, we design an embedding scheme and identify a lower bound on the number of wavelengths required, and provide a wavelength assignment algorithm which achieves the lower bound. Our result for this type of chordal ring is about half of that on WDM ring with the same number of nodes.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Arden, B., Lee, H.: Analysis of chordal ring networks. IEEE Transactions on Computers 30(4), 291–295 (1981)

    Article  MathSciNet  Google Scholar 

  2. Beauquier, B., Bermond, J.-C., Gargano, L., Hell, P., Pérennes, S., Vaccaro, U.: Graph problems arising from wavelength routing in all optical networks. In: Proceedings of WOCS 1997, pp. 366–370 (1997)

    Google Scholar 

  3. Bezrukov, S., Chavez, J., Harper, L., Rottger, M., Schroeder, U.-P.: The congestion of n-cube layout on a rectangular grid. Discrete Mathematics, 13–19 (2000)

    Google Scholar 

  4. Chen, Y., Shen, H.: Wavelength assignment for directional hypercube communications on a class of WDM optical networks. Tech. Rep. (2005)

    Google Scholar 

  5. Erbele, J.: The cyclic cutwidth of Q n , California State University San Bernardino (CSUSB), Tech. Rep. (2003)

    Google Scholar 

  6. Gardner, M.: Knotted Doughnuts And other Mathematical Entertainments. W.H. Freeman and Company, New York (1986)

    MATH  Google Scholar 

  7. Gu, Q.-P., Peng, S.: Multihop all-to-all broadcast on WDM optical networks. IEEE Trans. Parallel Distrib. Syst. 14(5), 477–486 (2003)

    Article  MathSciNet  Google Scholar 

  8. Leighton, F.T.: Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes. Morgan Kaufmann, San Francisco (1992)

    MATH  Google Scholar 

  9. Ruan, L., Du, D.-Z., Hu, X.-D., Jia, X., Li, D., Sun, Z.: Converter placement supporting broadcast in WDM optical networks. IEEE Transactions on Computers 50(7), 750–758 (2001)

    Article  MathSciNet  Google Scholar 

  10. Schroder, H., Schroder, H., Sykora, O., Vrto, I.: Cyclic cutwidths of the mesh. In: Bartosek, M., Tel, G., Pavelka, J. (eds.) SOFSEM 1999. LNCS, vol. 1725, pp. 443–452. Springer, Heidelberg (1999)

    Google Scholar 

  11. Yang, Y., Wang, J.: Cost-effective designs of WDM optical interconnects. IEEE Transactions on Parallel and Distributed Systems 16(1), 51–66 (2005)

    Article  Google Scholar 

  12. Yuan, X., Melhem, R.: Optimal routing and channel assignments for hypercube communication on optical mesh-like processor arrays. In: Proceedings of the 5th International Conference on Massively Parallel Processing Using Optical Interconnection IFIP International Conference on Network and Parallel Computing, pp. 110–118 (1998)

    Google Scholar 

  13. Zang, H., Jue, J.P., Mukherjee, B.: A review of routing and wavelength assignment approaches for wavelength-routed optical networks. Optical Network Magazine 1(1), 47–60 (2000)

    Google Scholar 

  14. Zhou, C., Yang, Y.: Wide-sense nonblocking multicast in a class of regular optical WDM networks. IEEE Transactions on Communications 50(1), 126–134 (2002)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Chen, Y., Shen, H., Zhang, H. (2006). Hypercube Communications on Optical Chordal Ring Networks with Chord Length of Three. In: Jesshope, C., Egan, C. (eds) Advances in Computer Systems Architecture. ACSAC 2006. Lecture Notes in Computer Science, vol 4186. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11859802_27

Download citation

  • DOI: https://doi.org/10.1007/11859802_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40056-1

  • Online ISBN: 978-3-540-40058-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics