Skip to main content
SpringerLink
Log in

Limited wavelength conversion in all-optical tree networks

  • Conference paper
  • First Online:
Automata, Languages and Programming (ICALP 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1443))

Included in the following conference series:

Abstract

Let T be a symmetric directed tree, i.e., a tree with each edge viewed as two opposite directed links. We consider the problem of routing arbitrary sets of connection requests in T. In all-optical communication tree networks with WDM (wavelength-division multiplexing) this is equivalent to color a given set of directed paths so that no two directed paths of the same color use the same link of T. Let W be the number of available wavelengths. The load, that is, the maximum number of directed paths passing through a link of T cannot exceed W. If there is no wavelength conversion available then each request (directed path) is restricted to a single wavelength and it is known that the minimum number of colors needed to color any set of directed paths in a tree is lower bounded away from the load L of the paths on the tree; moreover, no algorithm is known that uses a number of colors less than 5L/3. The presence of wavelength converters allows to overcome this limits. The complexity of converters is measured by the maximum degree, which represents the maximum number of possible conversions of any given wavelength. We show that it is possible to route any set of requests of load L ≤ W(1 − e), where ε depends only on the degree of the converters. Moreover, we show that in any tree it is possible to route any set of requests of load L <- W with converters of degree O(√W). In case of trees containing at most one node of degree ≥ 4 we show that converters of degree 3 already allow to route any set of requests of load L≤W.

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

Access this chapter

Log in via an institution

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, M. Sudan, “Efficient Routing and Scheduling Algorithms for Optical Networks”, in: Proceedings of the 5th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'94), (1994), 412–423.

    Google Scholar 

  2. V. Auletta, I. Caraggiannis, C. Kaklamanis, G. Persiano, “Bandwidth Allocation Algorithms on tree-Shaped All-Optical Networks with Wavelength Converters” SIROCCO'97.

    Google Scholar 

  3. V. Auletta, I. Caraggiannis, C. Kaklamanis, G. Persiano, “Optimal and Nearly-Optimal Wavelength Routing with Low-Degree Converters”, manuscript.

    Google Scholar 

  4. Y. Aumann and Y. Rabani, “Improved Bounds for All Optical Routing”, in: Proceedings of the 6th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'95), (1995), 567–576.

    Google Scholar 

  5. Y. Bartal, S. Leonardi, “On-Line Routing in All-Optical Networks”, Proceedings of 24th International Colloquium on Automata, Languages, and Programming (ICALP 97), Bologna, Italy, July 1997.

    Google Scholar 

  6. L. A. Bassalygo, “Asymptotically Optimal Switching Circuits, Problems of Information Transmission, 1981, 206–211.

    Google Scholar 

  7. 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), Geneve, Switzerland, April 1997

    Google Scholar 

  8. C. Berge, Graphs, North-Holland.

    Google Scholar 

  9. J.-C. Bermond, L. Gargano, S. Perennes, A.A. Rescigno, U. Vaccaro, “Efficient Collective Communication in Optical Networks”, Theoretical Compute Science, to appear.

    Google Scholar 

  10. F.R.K. Chung, Spectral Graph Theory, CBMS 92, American Mathematical Society, 1997.

    Google Scholar 

  11. T. Erlebach and K. Jansen. “Scheduling of Virtual Connections in Fast Networks”, Proc. of 4th Workshop on Parallel Systems and Algorithms PASA '96, (1996), 13–32.

    Google Scholar 

  12. L. Gargano, P. Hell, S. Perennes, “Colouring All Directed Paths in a Symmetric Tree with Applications to WDM Routing”, Proceedings of ICALP 97.

    Google Scholar 

  13. O. Gerstel, S. Kutten, R. Ramaswami and G. Sasaki, “Wavelength Conversion in All-Optical Ring Networks”, Proceedings of 6th Annual ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing (PODC'97).

    Google Scholar 

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

    Google Scholar 

  15. K. Kaklamanis G. Persiano, T. Erlebach, K. Jansen, “Constrained Bipartite Edge Coloring with Applications to Wavelength Routing” Proceedings of ICALP 97.

    Google Scholar 

  16. E. Kumar, E. Schwabe, “Improved Access to Optical Bandwidth in Trees”, Proceedings of SODA '97.

    Google Scholar 

  17. A. Lubotzky, R. Phillips, P. Sarnak, “Ramanujan Graphs”, Combinatorica, vol. 8, 1988, 261–278.

    Article  MATH  MathSciNet  Google Scholar 

  18. 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 

  19. A. D. McAulay, Optical Computer Architectures, John Wiley, 1991.

    Google Scholar 

  20. M. Mihail, K. Kaklamanis, S. Rao, “Efficient Access to Optical Bandwidth”, in: Proceedings of 36th Annual IEEE Symposium on Foundations of Computer Science (FOCS'95), (1995), 548–557.

    Google Scholar 

  21. P. Raghavan and E. Upfal, “Efficient Routing in All-Optical Networks”, in: Proceedings of STOC'94, (1994), 133–143.

    Google Scholar 

  22. R. Ramaswami, G.H. Sasaki, “Multiwavelength Optical Networks with Limited Wavelength Conversion” Proc. of IEEE Infocom 1997.

    Google Scholar 

  23. R. Ramaswami, “Multi-Wavelength Lightwave Networks for Computer Communication”, IEEE Communication Magazine, vol. 31, (1993), 78–88.

    Article  Google Scholar 

  24. V. Sharma and E. A. Varvarigos, “Limited wavelength translation in all-optical WDM mesh networks”, IEEE Infocom'98, to appear.

    Google Scholar 

  25. R.M. Tanner, “Explicit Construction of Concentrators from Generalized n-gons”, SIAM J. Alg. Discr. Meth., 5 (1984), 287–293.

    Article  MATH  MathSciNet  Google Scholar 

  26. R.J. Vetter and D.H.C. Du, “Distributed Computing with High-Speed Optical Networks”, IEEE Computer, vol. 26, (1993), 8–18.

    Google Scholar 

  27. G. Wilfong, P. Winkler, “Ring Routing and Wavelength Translation”, Proceedings of SODA '98, to appear.

    Google Scholar 

  28. J. Yates, J. Lacey, D. Everitt, M. Summerfield, “Limite Range Wavelength Translation in All-Optical Networks”, Proc. of IEEE Infocom 1996, pp. 954–961.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Informatica, Università di Salerno, 84081, Baronissi, SA, Italy

    Luisa Gargano

Authors
  1. Luisa Gargano
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Kim G. Larsen Sven Skyum Glynn Winskel

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Gargano, L. (1998). Limited wavelength conversion in all-optical tree networks. In: Larsen, K.G., Skyum, S., Winskel, G. (eds) Automata, Languages and Programming. ICALP 1998. Lecture Notes in Computer Science, vol 1443. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055083

Download citation

  • DOI: https://doi.org/10.1007/BFb0055083

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64781-2

  • Online ISBN: 978-3-540-68681-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation