On optimal traffic grooming in WDM rings

We consider the problem of designing a virtual topology to minimize electronic routing, that is, grooming traffic, in wavelength routed optical rings. The full virtual topology design problem is NP-hard even in the restricted case where the physical topology is a ring, and various heuristics have been proposed in the literature for obtaining good solutions, usually for different classes of problem instances. We present a new framework which can be used to evaluate the performance of heuristics and which requires significantly less computation than evaluating the optimal solution. This framework is based on a general formulation of the virtual topology problem, and it consists of a sequence of bounds, both upper and lower, in which each successive bound is at least as strong as the previous one. The successive bounds take larger amounts of computation to evaluate, and the number of bounds to be evaluated for a given problem instance is only limited by the computational power available. The bounds are based on decomposing the ring into sets of nodes arranged in a path and adopting the locally optimal topology within each set. While we only consider the objective of minimizing electronic routing in this paper, our approach to obtaining the sequence of bounds can be applied to many virtual topology problems on rings. The upper bounds we obtain also provide a useful series of heuristic solutions