The Traffic Grooming Problem in Optical Networks with Respect to ADMs and OADMs: Complexity and Approximation

All-optical networks transmit messages along lightpaths in which the signal is transmitted using same wavelength all relevant links. We consider problem of switching cost minimization these networks. Specifically, input to under consideration an optical network modeled by a graph G, set paths on and integer g termed grooming factor. One has assign (modeled color) every lightpath, so that edge used at most color. A lightpath operating some λ uses one Add/Drop multiplexer (ADM) both endpoints Optical (OADM) intermediate node, λ. Two lightpaths, λ, share ADMs OADMs their common nodes. Therefore, total due usage depends assignment. ring path topology function convex combination α·|OADMs|+(1−α)|ADMs| number deployed network. showed minimizing this NP-complete for combination, even with g=2. On positive side, we present polynomial-time approximation algorithm problem.