Optimal placement of wavelength converters in WDM optical networks with a general tree of rings topology

In wavelength routed optical networks, wavelength converters can potentially reduce the requirement on the number of wavelengths. The problem of placing a minimum number of wavelength converters in a WDM network so that any routing can be satisfied using no more wavelengths than if there were wavelength converters at every node was raised by Wilfong and Winkler (1998) as the minimum sufficient set problem. This problem is NP-complete in general WDM networks. Wan et al. (1999), showed that the problem is tractable if every edge in the network is bi-directed and the skeleton of the network is a tree of rings. We show that the minimum sufficient set problem is tractable in any directed graph with a general tree of rings skeleton.