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**1 - 2**of**2**### Abstract IYER, PRASHANT. The Complexity of Traffic Grooming in Optical Path Networks with Egress

"... We consider the problem of minimizing network costs when grooming traffic in optical networks that support Wavelength Division Multiplexing (WDM). While the general problem has been shown to be NP-Hard for a number of cost measures, there still exist restricted problems for which no complexity bound ..."

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We consider the problem of minimizing network costs when grooming traffic in optical networks that support Wavelength Division Multiplexing (WDM). While the general problem has been shown to be NP-Hard for a number of cost measures, there still exist restricted problems for which no complexity bound is known. In this research, we restrict our attention to traffic grooming for path networks with egress (all-to-one) traffic. This restricted model has practical significance for high speed (optical) access networks and can also lead to better bounds and approximations on more general network topologies (such as ring and star networks) that can be decomposed into path networks. Three important cost measures for this restricted model are studied. The first cost measure is the total number of ADMs used by the solution. Minimizing this cost was known to be NP-Complete even for egress traffic without using cross connects. We show that allowing an unbounded number of wavelengths obviates the need for digital cross connects at the nodes and hence the problem remains NP-Complete even when cross connects are allowed. The second cost measure is the number of transceivers used by the solution. We show that the problem of minimizing the number of transceivers is NP-Complete, even when restricted to egress traffic. We then develop a simple approximation scheme where the transceiver cost exceeds the

### Topology Design in WDM Rings to Minimize Electronic Routing: EÆcient Computation of Tight Bounds

"... We consider the problem of designing a virtual topology to minimize electronic routing, that is, grooming traÆc, 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 heuristics have been propose ..."

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We consider the problem of designing a virtual topology to minimize electronic routing, that is, grooming traÆc, 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 heuristics have been proposed in the literature. We present a new framework of bounds which can be used to evaluate the performance of heuristics, and which requires signi cantly less computation than evaluating the optimal solution. This framework 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 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. 1