Traffic Grooming in Unidirectional WDM Rings with Bounded Degree Request Graph

Traffic grooming is a major issue in optical networks. It refers to grouping low rate signals into higher speed streams, in order to reduce the equipment cost. In SONET WDM networks, this cost is mostly given by the number of electronic terminations, namely Add-Drop Multiplexers (ADMs for short). We consider the unidirectional ring topology with a generic grooming factor C, and in this case, in graph-theoretical terms, the traffic grooming problem consists in partitioning the edges of a request graph into subgraphs with at most C edges, while minimizing the total number of vertices of the decomposition. We consider the case when the request graph has bounded degree Δ, and our aim is to design a network (namely, place the ADMs at each node) being able to support any request graph with maximum degree at most Δ. The existing theoretical models in the literature are much more rigid, and do not allow such adaptability. We formalize the problem, and we solve the cases Δ = 2 (for all values of C) and Δ = 3 (except the case C = 4). We also provide lower and upper bounds for the general case.