Parallel Computing Using Optical Interconnections pp 117-136 | Cite as

# On Wavelength Assignment in WDM Optical Networks

Chapter

## Abstract

Routing and wavelength assignments are fundamental problems in efficient use of optical networks that employ wavelength division multiplexing of the fiber bandwidth. Three perspectives are taken in this chapter. First, the computational complexity of wavelength assignment is considered. Next, wavelength assignment with traffic restricted to all-to-all gossiping is examined, where lower bounds and an approximation algorithm are developed. Finally, results on the related problem of file transfer scheduling in optical networks are given for several network topologies.

## Keywords

Optical Network Wavelength Division Multiplex Connection Request Wavelength Assignment File Transfer## Preview

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## References

- [1]A. Aggarwal, A. Bar-Noy, D. Coppersmith, R. Ramaswami, B. Schieber, and M. Sudan, “Efficient Routing and Scheduling Algorithms for Optical Networks,”
*Proceedings of the ACM-SIAM Symposium on Discrete Algorithms SODA 1994*, pp. 412–423.Google Scholar - [2]S. Banerjee and C. Chen, “Design of Wavelength-Routed Optical Networks for Circuit Switched Traffic,”
*Proceedings of the IEEE Globecom’ 96*, London, November 1996.Google Scholar - [3]D. Banerjee and B. Mukherjee, “Practical Approaches for Routing and Wavelength Assignment in All-Optical Wavelength Routed Networks,”
*Proceedings IEEE Infocom’ 94*, Toronto, June 1994, pp. 110–119.Google Scholar - [4]D. Banerjee and B. Mukherjee, “A Practical Approach for Routing and Wavelength Assignment in Large Wavelength-Routed Optical Networks,”
*IEEE Journal on Selected Areas in Communications*, Vol 14,No 5, June 1996, pp. 903–908.CrossRefGoogle Scholar - [5]R. A. Barry and P. A. Humblet, “On the Number of Wavelengths and Switches in All-Optical Networks,”
*IEEE Transactions on Communications*, Vol 42,No 2/3/4, 1994, pp. 583–591.CrossRefGoogle Scholar - [6]B. Beauquier, J.C. Bermond, L. Gargano, P. Hell, S. Perennes, U. Vaccaro, “Graph Problems arising from Wavelength Routing in All Optical Networks,”
*Proceedings of the Second Workshop in Optics and Computer Science*, Geneva, Switzerland, April 1997.Google Scholar - [7]C. Chen and S. Banerjee, “A New Model for Optimal Routing and Wavelength Assignment in Wavelength Division Multiplexed Optical Networks,”
*Proceedings of IEEE Infocom’ 96*, San Francisco, April 1996, pp. 164–171.Google Scholar - [8]H. Choi, H.-A. Choi, and M. Azizo\( \tilde g \)lu, “Efficient Scheduling of Transmissions in Optical Broadcast Networks,”
*IEEE/ACM Transactions on Networking*, Vol. 14,No. 6, December 1996, pp. 913–920.CrossRefGoogle Scholar - [9]H.-A. Choi and S. L. Hakimi, “Scheduling File Transfers for Trees and Odd Cycles,”
*SIAM Journal on Computing*, Vol. 16,No. 1, February 1987, pp. 162–168.MATHCrossRefGoogle Scholar - [10]E. G. Coffman, Jr., M. R. Garey, D. S. Johnson, and A. S. LaPaugh, “Scheduling File Transfers,”
*SIAM Journal on Computing*, Vol. 14, 1985, pp. 744–780.MATHCrossRefGoogle Scholar - [11]T. Erlebach and K. Jansen, “The Complexity of Call-Scheduling in Trees, Rings, and Meshes,”
*30th Hawaii International Conference on System Sciences*, March 1997.Google Scholar - [12]M.R. Garey and D.S Johnson,
*Computers and Intractability, A Guide to the Theory of NP-Completeness*, W.H. Freeman and Company, 1979.Google Scholar - [13]E. Harder, “Routing and Wavelength Assignment in All-Optical WDM Wavelength Routing Networks,” D.Sc. dissertation, The George Washington University, 1998.Google Scholar
- [14]E. Harder. S.-K. Lee, H.-A. Choi, “On Wavelength Assignment in WDM Optical Networks,”
*Proceedings MPPOI’ 97*Montreal, Canada, June 1997.Google Scholar - [15]E. Harder. H.-A. Choi, “File Transfer in All-Optical Networks,” submitted to
*Proceedings MPPOI 98*, to be submitted to NETWORKS.Google Scholar - [16]M.C. Heydemann, J-C. Meyer, and D. Sotteau, “On Forwarding Indices of Networks,”
*Discrete Applied Mathematics*, Vol. 23, 1989, pp. 102–123.CrossRefGoogle Scholar - [17]D. Hochbaum, editor,
*Approximation Algorithms for NP-Hard Problems*, PWS Publishing Company, Boston, 1997.Google Scholar - [18]I. Holyer, “The NP-completeness of Edge-Coloring,”
*SIAM Journal on Computing*Vol. 10, 1981, pp. 718–720.MATHCrossRefGoogle Scholar - [19]K. Jansen, “Aproximation Results for Wavelength Routing in Directed Trees,”
*Proceedings of the Second Workshop in Optics and Computer Science*, Geneva, Switzerland, April 1997.Google Scholar - [20]R.M. Karp, “Reducibility Among Combinatorial Problems,”
*Complexity of Computer Computations*, R.E. Miller and J.W. Thatcher, editors, New York, Plenum Press, 1972.Google Scholar - [21]M. Kova\( \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{c} \)ević and A. S. Acampora, “Benefits of Wavelength Translation in All-Optical Clear-Channel Networks,”
*IEEE Journal on Selected Areas in Communications*, Vol. 14,No. 5, June 1996, pp. 868–880.Google Scholar - [22]V. Kumar and E. J. Schwabe, “Improved Access to Optical Bandwidth in Trees,”
*Proceedings of the Fifth ACM-SIAM Symposium on Discrete Algorithms SODA*, January, 1997.Google Scholar - [23]F. T. Leighton,
*Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes*, Morgan Kaufmann Publishers, 1992.Google Scholar - [24]W. Mao and R. Simha, “Routing and Scheduling File Transfers in Packet-Switched Networks,”
*Journal of Computing and Information*, Vol. 1, 1994, pp. 559–594.Google Scholar - [25]A. Mokhtar and M. Azizo\( \tilde g \)lu, “Dynamic Route Selection and Wavlength Assignment in All-Optical Networks,”
*LEOS*, 1995, pp. 220–221.Google Scholar - [26]B. Mukherjee,
*Optical Communication Networks*. McGraw-Hill, 1997.Google Scholar - [27]B. Mukherjee, S. Ramamurthy, D. Banerjee, and A. Mukherjee, “Some Principles for Designing Wide-Area Optical Networks,”
*Proceedings IEEE INFOCOM’ 94*, Toronto, 1994, pp. 110–119.Google Scholar - [28]P. Raghavan and E. Upfal, “Efficient Routing in All-Optical Networks,”
*Proceedings of the 26th ACM Symposium on the Theory of Computing STOC 1994*, 1994, pp. 134–143.Google Scholar - [29]R. Ramaswami and K. N. Sivarajan, “Optimal Routing and Wavelength Assignment in All-Optical Networks,”
*Proceedings IEEE INFOCOM’ 94*, Toronto, Canada, June 1994, pp. 970–983.Google Scholar - [30]R. Ramaswami and K. N. Sivarajan, “Routing and Wavelength Assignment in All-Optical Networks,”
*IEEE/ACM Transactions on Networking*, vol. 3,No. 5, October 1995, pp. 489–500.CrossRefGoogle Scholar - [31]S. Subramanian, M. Azizo\( \tilde g \)lu, and A. Somani, “Connectivity and Sparse Wavelength Conversion in Wavelength-Routing Networks,”
*Proceedings IEEE Infocom’ 96*, San Francisco, March 1996, pp. 148–155.Google Scholar - [32]S. Subramaniam and R. A. Barry, “Wavelength Assignment in Fixed Routing WDM Networks,”
*Proceedings of the IEEE International Conference on Communications’ 97*, May 1997, pp. 406–410.Google Scholar

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© Kluwer Academic Publishers 1998