Wavelength assignment in WDM rings to minimize SONET ADMs

We study wavelength assignment for lightpaths over WDM rings to minimize the SONET ADMs (add/drop multiplexers) used. This problem has attracted much attention recently. However, its computational complexity remains unknown, and the only known heuristic (Gerstel et al., 1998) which does not allow the splitting of lightpaths is problematic in terms of both the algorithm itself and its performance analysis. We first prove the NP-completeness of this problem, followed by a nontrivial randomized (3+e)/(1+e)-approximation scheme. We then present a tighter lower bound on the minimum number of ADMs required. After that, we show the incorrectness of the known heuristic and then modify it to make it correct. We also propose three additional heuristics. Their performances are compared through extensive simulation studies.