Skip to main content

Recent Advances in Wavelength Routing

  • Conference paper
  • First Online:
SOFSEM 2001: Theory and Practice of Informatics (SOFSEM 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2234))

  • 283 Accesses

Abstract

We study the problem of allocating optical bandwidth to sets of communication requests in all-optical networks that utilize Wavelength Division Multiplexing (WDM). WDM technology establishes communication between pairs of network nodes by establishing transmitter- receiver paths and assigning wavelengths to each path so that no two paths going through the same fiber link use the same wavelength. Optical bandwidth is the number of distinct wavelengths. Since state-of-the-art technology allows for a limited number of wavelengths, the engineering problem to be solved is to establish communication between pairs of nodes so that the total number of wavelengths used is minimized; this is known as the wavelength routing problem.

In this paper we survey recent advances in bandwidth allocation in tree- shaped WDM all-optical networks. We present hardness results and lower bounds for the general problem and the special case of symmetric communication. We also survey various techniques that have been developed recently, and explain how they can be used to attack the problem. First, we give the main ideas of deterministic greedy algorithms and study their limitations. Then, we show how to use various ways and models of wavelength conversion in order to achieve almost optimal bandwidth utilization. Finally, we show that randomization can help to improve the deterministic upper bounds.

This work was partially funded by the European Union under IST FET Project ALCOM-FT and Improving RTN Project ARACNE.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. Aggarwal, A. Bar-Noy, D. Coppersmith, R. Ramaswami, B. Schieber, and M. Sudan, Efficient Routing and Scheduling Algorithms for Optical Networks, Journal of the ACM, Vol. 43, No. 6, 1996, pp. 973–1001.

    Article  MATH  MathSciNet  Google Scholar 

  2. V. Auletta, I. Caragiannis, L. Gargano, C. Kaklamanis, P. Persiano. Sparse and Limited Wavelength Conversion in All-Optical Tree Networks. Theoretical Computer Science, to appear.

    Google Scholar 

  3. V. Auletta, I. Caragiannis, C. Kaklamanis, and P. Persiano, Randomized Path Coloring on Binary Trees. In Proc. of the 3rd International Workshop on Approximation Algorithms for Combinatorial Optimization (APPROX 2000), LNCS 1913, Springer, pp. 60–71, 2000.

    Google Scholar 

  4. V. Auletta, I. Caragiannis, C. Kaklamanis, and P. Persiano, Bandwidth Allocation Algorithms on tree-Shaped All-Optical Networks with Wavelength Converters. In Proc. of the 4th International Colloquium on Structural Information and Communication Complexity (SIROCCO’ 97), 1997, pp. 13–27.

    Google Scholar 

  5. V. Auletta, I. Caragiannis, C. Kaklamanis, and P. Persiano, Efficient Wavelength Routing in Trees with Low-Degree Converters. Multichannel Optical Networks: Theory and Practice, DIMACS Series on Discrete Mathematics and Theoretical Computer Science, vol. 46, AMS, pp. 1–13, 1998.

    MathSciNet  Google Scholar 

  6. V. Auletta, I. Caragiannis, C. Kaklamanis, and P. Persiano, On the Complexity of Wavelength Converters. In Proc. of the 23rd International Symposium on Mathematical Foundations of Computer Science (MFCS’ 98), LNCS 1450, Springer, 1998, pp. 771–779.

    Google Scholar 

  7. Y. Aumann and Y. Rabani, Improved Bounds for All Optical Routing. In Proc. of the 6th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA’ 95), 1995, pp. 567–576.

    Google Scholar 

  8. R. A. Barry, and P. A. Humblet, Models of Blocking Probability in All-Optical Networks with and without Wavelength Changers. IEEE Journal on Selected Areas of Communication, vol. 14, 1996, pp. 858–867.

    Article  Google Scholar 

  9. B. Beauquier, J.-C. Bermond, L. Gargano, P. Hell, S. Perennes, and U. Vaccaro, Graph Problems Arising from Wavelength-Routing in All-Optical Networks. 2nd Workshop on Optics and Computer Science (WOCS’ 97), 1997.

    Google Scholar 

  10. J.-C. Bermond, L. Gargano, S. Perennes, A.A. Rescigno, and U. Vaccaro, Efficient Collective Communication in Optical Networks. Theoretical Compute Science, 233 (1–2), 2000, pp. 165–189.

    Article  MATH  MathSciNet  Google Scholar 

  11. I. Caragiannis, C. Kaklamanis, and P. Persiano. Wavelength Routing of Symmetric Communication Requests in Directed Fiber Trees. In Proc. of the 5th InternationalColloquium on Structural Information and Communication Complexity (SIROCCO 98), pp. 10–19, 1998.

    Google Scholar 

  12. I. Caragiannis, C. Kaklamanis, and P. Persiano. Edge Coloring of Bipartite Graphs with Constraints. In Proc. of the 23rd International Symposium on Mathematical Foundations of Computer Science (MFCS 99), LNCS1450, Springer, pp. 771–779, 1999. Also, Theoretical Computer Science, to appear.

    Google Scholar 

  13. I. Caragiannis, C. Kaklamanis, P. Persiano. Bounds on Optical Bandwidth Allocation in Directed Fiber Tree Topologies. 2nd Workshop on Optics and Computer Science, 1997.

    Google Scholar 

  14. T. Erlebach and K. Jansen. Scheduling of Virtual Connections in Fast Networks. In Proc. of 4th Workshop on Parallel Systems and Algorithms (PASA’ 96), World Scientific, 1997, pp. 13–32.

    Google Scholar 

  15. T. Erlebach, K. Jansen. Call Scheduling in Trees, Rings and Meshes. In Proc. of the 30th Hawaii International Conference on System Sciences, 1997.

    Google Scholar 

  16. T. Erlebach, K. Jansen, C. Kaklamanis, M. Mihail and P. Persiano OptimalWavelength Routing on Directed Fiber Trees Theoretical Computer Science 221, 1999, pp. 119–137.

    Article  MATH  MathSciNet  Google Scholar 

  17. L. Gargano, Limited Wavelength Conversion in All-Optical Tree Networks. In Proc. of the 25th International Colloquium on Automata, Languages, and Programming (ICALP’ 98), LNCS 1443, Springer, pp. 544–555.

    Google Scholar 

  18. P. E. Green, Fiber-Optic Communication Networks. Prentice-Hall, 1992.

    Google Scholar 

  19. K. Jansen. Approximation Results for Wavelength Routing in Directed Binary Trees. 2nd Workshop on Optics and Computer Science, 1997.

    Google Scholar 

  20. C. Kaklamanis and P. Persiano, Efficient Wavelength Rouiting in Directed Fiber Trees. In Proc. of the 4th European Symposium on Algorithms (ESA’ 96), LNCS 1136, Springer, pp. 460–470.

    Google Scholar 

  21. C. Kaklamanis, P. Persiano, T. Erlebach, K. Jansen Constrained Bipartite Edge Coloring with Applications to Wavelength Routing. In Proc. of the 24th International Colloquium on Automata, Languages, and Programming (ICALP’ 97), LNCS 1256, Springer, pp. 493–504, 1997.

    Google Scholar 

  22. R. Klasing, Methods and Problems of Wavelength-Routing in All-Optical Networks. In Proc. of MFCS 98 Workshop on Communication, pp. 1–9, 1998.

    Google Scholar 

  23. J. Kleinberg and A. Kumar, Wavelength Conversion in Optical Networks. In Proc. of the 10th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA’ 99), pp. 566–575, 1999.

    Google Scholar 

  24. M. Kovacevic and S. Acampora, Benefits of wavelength Translation in All-Optical Clear-Channel Networks. IEEE Journal on Selected Areas of Communication, vol. 14, 1996, pp. 868–880.

    Article  Google Scholar 

  25. E. Kumar and E. Schwabe, Improved Access to Optical Bandwidth in Trees. In Proc. of the 8th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA’ 97), 1997, pp. 437–444.

    Google Scholar 

  26. K.-C. Lee and V.O.K. Li, Routing and Switching in a wavelength convertible lightwave network. In Proc. of IEEE INFOCOM 1993, 1993, pp. 578–585.

    Google Scholar 

  27. A. Lubotzky, R. Phillips, and P. Sarnak, Ramanujan Graphs. Combinatorica, vol. 8, 1988, pp. 261–278.

    Article  MATH  MathSciNet  Google Scholar 

  28. G.A. Margulis, Explicit Group-Theoretic Constructions of Combinatorial Schemes and their Applications for the Construction of Expanders and Concentrators. Problemy Peredaci Informacii, 1988.

    Google Scholar 

  29. M. Mihail, K. Kaklamanis, and S. Rao, Efficient Access to Optical Bandwidth. In Proc. of 36th Annual IEEE Symposium on Foundations of Computer Science (FOCS’ 95), 1995, pp. 548–557.

    Google Scholar 

  30. R. Pankaj, Architectures for Linear Lightwave Networks. PhD. Thesis, Department of Electrical Engineering and Computer Science, MIT, Cambridge MA, 1992.

    Google Scholar 

  31. Y. Rabani, Path Coloring on the Mesh, In Proc. of the 37th IEEE Symposium on Foundations of Computer Science (FOCS 96), pp. 400–409, 1996.

    Google Scholar 

  32. J. Radhakrishnan and A. Ta-Shma, Tight Bounds for Depth-Two Super concentrators. In Proc. of the 38th Annual IEEE Symposium on Foundations of Computer Science, 1997, pp. 585–594.

    Google Scholar 

  33. P. Raghavan and E. Upfal, Efficient Routing in All-Optical Networks. In Proc. of the 26th Annual ACM Symposium on the Theory of Computing (STOC’ 94), 1994, pp. 133–143.

    Google Scholar 

  34. B. Ramamurthy and B. Mukherjee, Wavelength Conversion in WDM Networking. IEEE J. on Selected Areas of Communication, vol. 16, 1998, pp. 1061–1073.

    Article  Google Scholar 

  35. R. Ramaswami and G.H. Sasaki, Multiwavelength Optical Networks with Limited Wavelength Conversion. In ACM/IEEE Trans. Networking, vol. 6, n. 6, 1998, pp. 744–754.

    Article  Google Scholar 

  36. R. Ramaswami and K. Sivarajan, Routing and wavelength Assignment in All-Optical Networks. In ACM/IEEE Trans. Networking, vol. 3, n. 5, 1995, pp. 489–500.

    Article  Google Scholar 

  37. R. Ramaswami, K. Sivarajan, Optical Networks. Morgan Kauffman Publishers, 1998.

    Google Scholar 

  38. M. Sipser, Expanders, Randomness, or Time versus Space. Journal of Computer and System Sciences, vol. 36, n. 3, 1988, pp. 379–383.

    Article  MATH  MathSciNet  Google Scholar 

  39. S. Subramaniam, M. Azizoglu, and A.K. Somani, All-Optical Networks with Sparse wavelength Conversion. ACM/IEEE Trans. on Networking, vol. 4, n. 4, 1996, pp. 544–557.

    Article  Google Scholar 

  40. A. Ta-Shma, Almost Optimal Dispersers. In Proc. of the 30th Annual ACM Symposium on the Theory of Computing (STOC’ 98), 1998, pp. 196–202.

    Google Scholar 

  41. G. Wilfong and P. Winkler, Ring Routing and Wavelength Translation. In Proc. of the 9th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA’ 98), 1998, pp. 333–341.

    Google Scholar 

  42. J. Yates, J. Lacey, D. Everitt, and M. Summerfield, Limited Range Wavelength Translation in All-Optical Networks. In Proc. of IEEE INFOCOM’ 96, 1996, pp. 954–961.

    Google Scholar 

  43. J. Zhou, N. Park, K. Vahala, M. Newkirk, and B. Miller, Four-Wave Mixing Wavelength Conversion Efficiency in Semicinductor Travelling-Wave Amplifiers Measured to 65 nm of Wavelength Shift. IEEE Phot. Tech. Letters, vol. 6, n. 8, 1994, pp. 984–987.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kaklamanis, C. (2001). Recent Advances in Wavelength Routing. In: Pacholski, L., Ružička, P. (eds) SOFSEM 2001: Theory and Practice of Informatics. SOFSEM 2001. Lecture Notes in Computer Science, vol 2234. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45627-9_5

Download citation

  • DOI: https://doi.org/10.1007/3-540-45627-9_5

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42912-8

  • Online ISBN: 978-3-540-45627-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics