On the complexity of wavelength converters

  • Vincenzo Auletta
  • Ioannis Caragiannis
  • Christos Kaklamanis
  • Pino Persiano
Contributed Papers Communication - Computable Real Numbers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1450)

Abstract

In this paper we present a greedy wavelength routing algorithm that allocates a total bandwidth of w(l) wavelengths to any set of requests of load l (where load is defined as the maximum number of requests that go through any directed fiber link) and we give sufficient conditions for correct operation of the algorithm when applied to binary tree networks. We exploit properties of Ramanujan graphs to show that (for the case of binary tree networks) our algorithm increases the bandwidth utilized compared to the algorithm presented in [3]. Furthermore, we use another class of graphs called dispersers, to implement wavelength converters of asymptotically optimal complexity with respect to their size (the number of all possible conversions). We prove that their use leads to optimal and nearly-optimal bandwidth allocation even in a greedy manner.

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References

  1. 1.
    V. Auletta, I. Caragiannis, C. Kaklamanis, P. Persiano, “Bandwidth Allocation Algorithms on Tree-Shaped All-Optical Networks with Wavelength Converters”. In Proc. of SIROCCO '97, 1997.Google Scholar
  2. 2.
    V. Auletta, I. Caragiannis, C. Kaklamanis, P. Persiano, “Efficient Wavelength Routing in Trees with Low-Degree Converters”. In Proc. of the DIMACS Workshop on Optical Networks, 1998, to appear.Google Scholar
  3. 3.
    L. Gargano, “Limited Wavelength Conversion in All-Optical Tree Networks”. In Proc. of ICALP '98, 1998, to appear.Google Scholar
  4. 4.
    C. Kaklamanis, P. Persiano, “Efficient Wavelength Routing on Directed Fiber Trees”. In Proc. of the 4th European Symposium on Algorithms (ESA '96), LNCS, Springer Verlag, 1996, pp. 460–470.Google Scholar
  5. 5.
    C. Kaklamanis, P. Persiano, T. Erlebach, K. Jansen, “Constrained Bipartite Edge Coloring with Applications to Wavelength Routing”. In Proc. of ICALP '97, LNCS 1256, Springer Verlag, 1997, pp. 493–504.Google Scholar
  6. 6.
    V. Kumar, E. Schwabe, “Improved Access to Optical Bandwidth in Trees”. In Proc. of the 8th Annual ACM-SIAM Symposium on Discrete Algorithms, 1997.Google Scholar
  7. 7.
    A. Lubotsky, R. Philipps, P. Sarnak, “Ramanujan Graphs”. Combinatorica, vol. 8, pp. 261–278, 1988.MathSciNetCrossRefGoogle Scholar
  8. 8.
    M. Mihail, C. Kaklamanis, S. Rao, “Efficient Access to Optical Bandwidth”. In Proc. of the 36th Annual Symposium on Foundations of Computer Science, pp. 548–557, 1995.Google Scholar
  9. 9.
    J. Radhakrishnan, A. Ta-Shma, “Tight Bounds for Depth-Two Superconcentrators”. In Proc. of the 38th Annual Symposium on Foundations of Computer Science, 1997.Google Scholar
  10. 10.
    P. Raghavan, E. Upfal, “Efficient Routing in All-Optical Networks”. In Proc. of the 26th Annual ACM Symposium on the Theory of Computing, 1994, pp. 133–143.Google Scholar
  11. 11.
    M. Sipser, “Expanders, randomness, or time versus space”. Journal of Computer and System Sciences, 36:379–383, 1988.MATHMathSciNetCrossRefGoogle Scholar
  12. 12.
    A. Ta-Shma, “Almost Optimal Dispersere”. In Proc. of STOC '98, 1998, to appear.Google Scholar

Copyright information

© Springer-Verlag 1998

Authors and Affiliations

  • Vincenzo Auletta
    • 1
  • Ioannis Caragiannis
    • 2
  • Christos Kaklamanis
    • 2
  • Pino Persiano
    • 1
  1. 1.Dipartimento di Informatica ed Appl.Université di SalernoBaronissiItaly
  2. 2.Computer Technology Institute Dept. of Computer Engineering and InformaticsUniversity of PatrasRioGreece

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