Optimal wavelength assignment in the implementation of parallel algorithms with ternary n-cube communication pattern on mesh optical network

Multi-ary n-cubes are a class of communication patterns that are employed by a number of typical parallel algorithms. This paper addresses the implementation of parallel algorithms with bidirectional and unidirectional ternary n-cube communication patterns on a mesh WDM optical network. For each of these two communication patterns, a routing and wavelength assignment scheme is described, and the number of wavelengths required is shown to attain the minimum, which guarantees the optimality of the proposed scheme.