We consider all-optical networks with shortest-path routing that use wavelength-division multiplexing and employ wavelength conversion at specific nodes in order to maximize their capacity usage. We present efficient algorithms for deciding whether a placement of wavelength converters allows the network to run at maximum capacity, and for finding an optimal wavelength assignment when such a placement of converters is known. Our algorithms apply to both undirected and directed networks. Furthermore, we show that the problem of designing such networks, i.e., finding an optimal placement of converters, is MAX SNP-hard in both the undirected and the directed case. Finally, we give a linear-time algorithm for finding an optimal placement of converters in undirected triangle-free networks, and show that the problem remains NP-hard in bidirected triangle-free planar networks.
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Erlebach, T., Stefanakos, S. Wavelength Conversion in All-Optical Networks with Shortest-Path Routing. Algorithmica 43, 43–61 (2005). https://doi.org/10.1007/s00453-005-1157-y
- Wavelength assignment
- Wavelength converter placement
- Graph algorithm
- Edge coloring
- Sufficient set