@article{iyer_dutta_savage_2009, title={Minimizing transceivers in optical path networks}, volume={8}, ISSN={["1536-5379"]}, DOI={10.1364/JON.8.000454}, abstractNote={The problem of routing traffic on multihop clear optical channels and deciding the virtual topology of optical channels to form on a physical network of fibers to minimize the cost of electronic switching equipment has become known as traffic grooming in optical networks. Traffic grooming is recognized as an important research area, because the joint opto-electric routing problem is a hard one, yet necessary because of the large cost of pure electronic switching. This problem has been shown to be NP-complete (nondeterminstic polynomial complete) even for very simple practical topologies such as a path network. In previous work, we have shown that at least the subproblem of routing traffic on a given virtual topology to minimize electronic switching (NP-hard for path networks with arbitrary traffic matrices) becomes polynomial when the traffic on the path is restricted to be egress traffic, that is, all traffic requests are destined for a single egress node. In that work, the objective was to minimize the raw OEO (opto-electro-optic) metric (number of bits electronically switched per second) totaled over all network nodes. Of late, it has become clear that electronic switching equipment cost is best counted in quantized units, e.g., in the number of transceiver interfaces at network nodes. In this paper, we consider the traffic grooming problem in unidirectional, WDM path networks with the goal of minimizing the number of transceivers. We conclusively show that the problem is NP-hard, even under the restriction of the egress traffic model. In the case of egress traffic, we give a simple heuristic that will never be worse than twice the optimal.}, number={5}, journal={JOURNAL OF OPTICAL NETWORKING}, author={Iyer, Prashant and Dutta, Rudra and Savage, Carla D.}, year={2009}, month={May}, pages={454–461} }
 @article{iyer_dutta_savage_2007, title={Complexity of path traffic grooming}, volume={6}, ISSN={["1536-5379"]}, DOI={10.1364/JON.6.001270}, abstractNote={Feature Issue on Transmission in Optically Transparent Core NetworksThe problem of efficiently designing lightpaths and routing traffic on them in hybrid electro-optic data communication networks so that optical pass-through is maximized and the electronic switching cost is minimized is known as traffic grooming and has been studied extensively. Traffic grooming is known to be an inherently difficult problem. It has been shown to be NP-complete even for path networks, a simple topology in which lightpath wavelength assignment is tractable. In this paper, we explore the borderline between tractability and intractability by considering grooming in unidirectional path networks in which all traffic requests are destined for a single egress node. Whether the complete grooming problem is NP-hard with this restriction is an open question. We show that at least the problem of routing traffic on a given virtual topology to minimize electronic switching (NP-hard for path networks with arbitrary traffic matrices) becomes polynomial on the egress model. We also show that in the egress model, if the capacity constraint is relaxed, the entire problem becomes polynomial. If, in addition, traffic requests are uniform, we provide an explicit combinatorial formula for the optimum solution as well as an algorithm that constructs a routing that achieves this optimum. For the case of finite capacity and unit traffic requests, we show how to polynomially find a feasible solution that is optimal under reasonable assumptions.}, number={11}, journal={JOURNAL OF OPTICAL NETWORKING}, author={Iyer, Prashant and Dutta, Rudra and Savage, Carla D.}, year={2007}, month={Nov}, pages={1270–1281} }