Publication 2001 Issue No. 7 - July Abstract - Converter Placement Supporting Broadcast in WDM Optical Networks
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Converter Placement Supporting Broadcast in WDM Optical Networks
July 2001 (vol. 50 no. 7)
pp. 750-758
 ASCII Text x 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.
 BibTex x @article{ 10.1109/12.936240,author = {Lu Ruan and Dingzhu Du and Xiaodong Hu and Xiaohua Jia and Deying Li and Zheng Sun},title = {Converter Placement Supporting Broadcast in WDM Optical Networks},journal ={IEEE Transactions on Computers},volume = {50},number = {7},issn = {0018-9340},year = {2001},pages = {750-758},doi = {http://doi.ieeecomputersociety.org/10.1109/12.936240},publisher = {IEEE Computer Society},address = {Los Alamitos, CA, USA},}
 RefWorks Procite/RefMan/Endnote x TY - JOURJO - IEEE Transactions on ComputersTI - Converter Placement Supporting Broadcast in WDM Optical NetworksIS - 7SN - 0018-9340SP750EP758EPD - 750-758A1 - Lu Ruan, A1 - Dingzhu Du, A1 - Xiaodong Hu, A1 - Xiaohua Jia, A1 - Deying Li, A1 - Zheng Sun, PY - 2001KW - Network optimizationKW - optical networksKW - WDMKW - converter placementKW - Color-CoveringKW - Vertex Color-Covering.VL - 50JA - IEEE Transactions on ComputersER -

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.

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