Optimal bandwidth utilization of all-optical ring with a converter of degree 4

In many models of all-optical routing, a set of communication paths in a network is given, and a wavelength is to 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 use the optical bandwidth efficiently. If a node of a network contains a wavelength converter, any path that passes through this node may change its wavelength. Having converters at some of the nodes can reduce the number of wavelengths required for routing. This paper presents a wavelength converter with degree 4 and gives a routing algorithm which shows that any routing with load L can be realized with L wavelengths when a node of an all-optical ring hosts such a wavelength converter. It is also proved that 4 is the minimum degree of the converter to reach the full utilization of the available wavelengths if only one node of an all-optical ring hosts a converter.