A Low Bound for Broadcast in Optical Networks of Bounded Treewidth Using Fewest Converters

Wavelengths and converters are shared by communication requests in optical networks. The usage of converters increases the utilization of wavelengths and allows more requests to succeed. The converters usage problem (CUP) is to determine the minimum number of converter so that each node can send messages to all the others (broadcasting). In this paper, we study the CUP in sparse conversion networks with bounded treewidth. A converter wavelength-dominates a node if there is a uniform wavelength path between them. The minimal wavelength dominating set problem (MWDSP) is to locate the minimum number of converters so that all the other nodes in the network are wavelength-dominated. We use a linear complexity dynamic programming algorithm to solve the MWDSP for networks with bounded treewidth. One such solution provides a low bound for the optimal solution to the CUP.