Multiwavelength Optical Networks pp 89-124 | Cite as

# Placement of Wavelength Converters

## Abstract

The number of wavelengths available in a network is always limited due to the restriction of hardware structure of optical routers/switches. An important goal of the design of WDM networks is to use less wavelengths to serve more communication needs. There are two basic approaches to achieving the goal. The first one is to find the proper routing and wavelength assignment methods, that is the routing and wavelength assignment problem (RWAP) discussed in Chapter 3. In this chapter we will focus on the second approach, that is to use of wavelength converters. Existing study has shown that the more converters installed in a network, the less number of wavelengths is needed, given the same network load (the maximal number of channels over a link). In fact, by using enough number of wavelength converters at the network nodes, the number of wavelengths required can be made equal to the network load, this is most ideal situation that we can expect since the number of wavelengths required in a system is no less than the network load. A simple example of achieving this feature, called the *Load-Wavelength Assignability* (LWA), is to equip every node in the network with a wavelength converter. However, it is too expensive to do so, because this will not only increase the cost of network hardware but also the complexity of routing and wavelength assignment.

## Keywords

Network Load Optimal Placement Wavelength Conversion Wavelength Assignment Wavelength Converter## Preview

Unable to display preview. Download preview PDF.

## References

- [1]V. Bafna, P. Berman, and T. Fujito, A 2-approximation algorithm for the undirected feedback vertex set problem,
*SIAM Journal on Discrete Mathematics*, 12 (3) (1999), 289–297.MathSciNetMATHCrossRefGoogle Scholar - [2]S. A. Cook, The complexity of theorem-proving procedures,
*Proceedings of the 3rd Annual ACM Symposium on Theory of Computing*(STOC), (1971), 151–158.Google Scholar - [3]J. M. H. Elmirghani and H. T. Moutfah, All-optical wavelength conversion technologies and applications in WDM networks,
*IEEE Communication Magazine*, 38 (3) (2000), 86–92.CrossRefGoogle Scholar - [4]F. Gavril, Algorithms for minimum coloring, maximum clique, minimum covering by cliques, and maximum independent set of a chordal graph,
*SIAM Journal on Computing*, 1 (1972), 180–187.MathSciNetMATHCrossRefGoogle Scholar - [5]X.-H. Jia, D.-Z. Du, X.-D. Hu, H.-J. Huang, and D.-Y. Li, Optimal placement of wavelength converters in WDM networks for parallel and distributed computing systems,
*Proceedings ofthe 4th International Conference on Algorithms and Architectures for Parallel Processing*, (2000), 548–559.Google Scholar - [6]X.-H. Jia, D.-Z. Du, X.-D. Hu, H.-J. Huang, and D.-Y. Li, Placement of Wavelength Converters for Minimal Wavelength Usage in WDM Networks,
*Proceedings of IEEE Conference on Computer Communications*(INFOCOM), 2002.Google Scholar - [7]E. Karasan and E. Ayanoglu, Effects of wavelength routing and selection algorithms on wavelength conversion gain in WDM optical networks,
*IEEE/ACM Transactions on Networking*, 6 (2) (1998), 186–196.CrossRefGoogle Scholar - [8]R. M. Karp, Reducibility among combinatorial problems, in R. E. Miller and J. W. Thatcher (eds.),
*Complexity of Computer Computations*, Plenum Press, New York, 85–103.Google Scholar - [9]J. Kleinberg and A. Kumar, Wavelength conversion in optical networks,
*Journal ofAlgorithms*, 38 (1) (2001), 25–50.MathSciNetMATHCrossRefGoogle Scholar - [10]D. König, Über graphen und ihre anwendung auf determinantentheorie und mengenlehre,
*Mathematische Annalen*, 77 (1916), 453–465.MathSciNetMATHCrossRefGoogle Scholar - [11]F. L. Luccio, Almost exact minimum feedback vertex set in meshes and butterflies,
*Information Processing Letters*, 66 (2) (1998), 59–64.MathSciNetMATHCrossRefGoogle Scholar - [12]B. Monien and E. Speckenmeyer, Ramsey numbers and an approximation algorithm for the vertex cover problem,
*Acta Informatica*, 22 (1985), 115–123.MathSciNetMATHCrossRefGoogle Scholar - [13]R. Ramaswami and G. Sasaki, Multiwavelength optical networks with limited wavelength conversion,
*IEEE/ACM Transactions on Networking*, 6 (6) (1998), 744–754.CrossRefGoogle Scholar - [14]C. Savage, Depth first search and the vertex cover problem,
*Information Processing Letters*, 14 (1982), 233–235.MathSciNetMATHCrossRefGoogle Scholar - [15]G. Wilfong and P. Winkler, Ring routing and wavelength translation,
*Proceedings of the 9th Annual ACM-SIAM Symposium on Discrete Algorithms*(SODA), (1998), 333–341.Google Scholar