Optimal Bandwidth Utilization of All-Optical Ring with a Converter of Degree 4

In many models of all-optical routing, a set ofcommunication paths in a network is given, and a wavelength is to beassigned to each path so that paths sharing an edge receive differentwavelengths. The goal is to assign as few wavelengths as possible, inorder to use the optical bandwidth efficiently. If a node of a networkcontains a wavelength converter, any path that passes through this nodemay change its wavelength. Having converters at some of the nodes canreduce the number of wavelengths required for routing. This paperpresents a wavelength converter with degree 4 and gives a routingalgorithm which shows that any routing with load L can berealized with L wavelengths when a node of an all-optical ringhosts such a wavelength converter. It is also proved that 4 isthe minimum degree of the converter to reach the full utilization ofthe available wavelengths if only one node of an all-optical ring hostsa converter.