Optimal placement of wavelength converters in trees, tree-connected rings, and tree of rings

In wavelength routed optical networks, wavelength converters can potentially reduce the requirement on the number of wavelengths. A recent study [Proceedings of 9th ACM-SIAM Symposium on Discrete Algorithms (1998)] raised the following problem: choose a minimum number of nodes in a WDM network to place wavelength converters so that any set of paths requires the same number of wavelengths as if wavelength converters were placed at all node. This problem is referred to as minimum sufficient set problem. It was shown to be NPcomplete in general WDM networks [Proceedings of 9th ACM-SIAM Symposium on Discrete Algorithms (1998)], and be as hard as the well-known minimum vertex cover problem [Proceedings of 10th ACM-SIAM Symposium on Discrete Algorithms (1999)]. In this paper, we extend their study in trees, tree-connected rings, and tree of rings which are widely used topologies in the telecommunications industry. We show that the optimal wavelength converter placement problem in these two practical topologies are tractable. Efficient polynomial-time algorithms are presented. q 2002 Published by Elsevier Science B.V.