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Converter Placement Supporting Broadcast in WDM Optical Networks
July 2001 (vol. 50 no. 7)
pp. 750-758

Abstract—Given a WDM optical network with wavelength channels on its fiber links, we consider the problem of finding the minimum set of network nodes such that, with wavelength converters at these nodes, broadcast can be supported in the network. We call this problem the Converter Placement problem. We model a given network using a graph $G$ with colors on its edges and give a mathematical formulation for the problem based on the graph model. Two related problems, Color-Covering and Vertex Color-Covering, are given and analyzed. Both of them are shown to have a polynomial-time approximation with performance ratio $\ln n + 1$ and $\ln n$ is the best possible performance ratio unless $NP \subset DTIME(n^{poly\log n})$, where $n$ is the number of vertices in $G$. Using these results, we show that the Converter Placement problem has a polynomial-time approximation with performance ratio $2(\ln n +1)$ and ${\frac{1}{2}}\ln n$ is the best possible performance ratio unless $NP \subset DTIME(n^{poly\log n})$. We present an approximation algorithm to solve the Converter Placement problem and study the performance of the algorithm on randomly generated network topologies.

[1] C.A. Brackett, "Dense Wavelength Division Multiplexing Networks: Principles and Applications," IEEE J. Selected Areas in Comm., vol. 8, no. 6, pp. 948-964, 1990.
[2] C. Lund and M. Yannakakis, “On the Hardness of Approximating Minimization Problems,” J. ACM, vol. 41, no. 5, pp. 960-981, Sept. 1994.
[3] R. Raz and S. Safra, “A Sub-Constant Error-Probability Low-Degree Test, and a Sub-Constant Error-Probability PCP Characterization of NP,” Proc. 29th Symp. Theory of Computing (STOC), pp. 475-484, May 1997.
[4] M. Kovacevic and A. Acampora, “Benefits of Wavelength Translation in All-Optical Clear-Channel Networks,” IEEE J. Selected Areas in Comm., vol. 14, pp. 868-880, June 1996.
[5] R. Ramaswami and K.J. Sivarajan, “Routing and Wavelength Assignment in All-Optical Networks,” IEEE/ACM Trans. Networking, vol. 3, no. 5, pp. 489-500, Oct. 1995.
[6] B. Ramamurthy and B. Mukherjee, “Wavelength Conversion in WDM Networking,” IEEE J. Selected Areas in Comm., vol. 16, no. 7, pp. 1061-1073, Sept. 1998.
[7] T.E. Stern and K. Bala, Multiwavelength Optical Networks: A Layered Approach. Reading, Mass.: Addison-Wesley, 1999.
[8] L.H. Sahasrabuddhe and B. Mukherjee, “Light-Trees: Optical Multicasting for Improved Performance in Wavelength-Routed Networks,” IEEE Comm. Magazine, vol. 37, no. 2, pp. 67-73, Feb. 1999.
[9] D. Li, X. Du, X. Hu, L. Ruan, and X. Jia, “Minimizing Number of Wavelengths in Multicast Routing Trees in WDM Networks,” Networks, vol. 35, no. 4, pp. 260-265, July 2000.
[10] X. Zhang, J. Wei, and C. Qiao, “Constrained Multicast Routing in WDM Networks with Sparse Light Splitting,” Proc. INFOCOM 2000, pp. 1781-1790, Mar. 2000.
[11] R.K. Pankaj, “Wavelength Requirements for Multicasting in All-Optical Networks,” IEEE/ACM Trans. Networking, vol. 7, no. 3, pp. 414-424, June 1999.
[12] N. Sreenath, K. Satheesh, G. Mohan, and C. Murthy, “Virtual Source Based Multicast Routing in WDM Optical Networks,” Proc. Int'l Conf. Networking (ICON) 2000, pp. 385-389, Sept. 2000.
[13] G. Xiao and Y.W. Leung, “Algorithms for Allocating Wavelength Converters in All-Optical Network,” IEEE/ACM Trans. Networking, vol. 7, no. 4, pp. 545-557, Aug. 1999.
[14] S. Thiagarajan and A.K. Somani, “An Efficient Algorithm for Optimal Wavelength Converter Placement on Wavelength-Routed Networks with Arbitrary Topologies,” Proc. INFOCOM '99, pp. 916-923, Mar. 1999.
[15] S. Subramaniam, M. Azizoglu, and A.K. Somani, “On Optimal Converter Placement in Wavelength-Routed Networks,” IEEE/ACM Trans. Networking, vol. 7, no. 5, pp. 754-766, Oct. 1999.

Index Terms:
Network optimization, optical networks, WDM, converter placement, Color-Covering, Vertex Color-Covering.
Citation:
Lu Ruan, Dingzhu Du, Xiaodong Hu, Xiaohua Jia, Deying Li, Zheng Sun, "Converter Placement Supporting Broadcast in WDM Optical Networks," IEEE Transactions on Computers, vol. 50, no. 7, pp. 750-758, July 2001, doi:10.1109/12.936240
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