Abstract:In many models of optical routing, a set of communication paths (req uests) in a network are given, and a wavelength must be assigned to each path so that paths sharing an edge receive different wavelengths. The goal is to assign as few wavelengths as possible, in order to make as efficient use as possible of the optical bandwidth. Much work in the area has considered the use of wavelen gth converters: if a node of a network contains a converter, any path passing th rough this node may change its wavelength. Having converters at some of the nodes can reduce the number of wavelengths down to congestion bound. Thus Wilfong and Winkler defined a set S of nodes to be sufficient if, placing converters at the nodes in S, every set of paths can be routed with a number of wavelengths equal to its congestion bound. In this paper, the minimum sufficient set problem in bi-directed networks is studied. The problem is transformed into minimum vertex cover problem and some algorithms are developed for the problem.