Optimal routing and wavelength assignment for augmented cubes in linear array optical networks

The augmented cube is a class of communication patterns that are employed by a number of typical parallel algorithms. It is one of the hypercube variations, and retains all favorable properties of hypercube. This paper addresses the routing and wavelength assignment for the augmented cube communication pattern in a linear array WDM optical network. By using congestion estimation and giving a routing and wavelength assignment strategy, we prove that the optimal number of wavelengths is ⌊4(N - 1)/3⌋, where N denotes the size of the augmented cube.