Implementing duplex crossed cube communication patterns on optical linear arrays

Crossed cubes are a class of promising parallel communication patterns. This paper addresses the issue of how to implement a half-duplex or full-duplex crossed cube on a WDM optical network with linear array topology. For either of these two communication patterns, a routing scheme, that is an embedding scheme, is proposed, and a wavelength assignment scheme under the embedding scheme is designed. The number of required wavelengths under the embedding scheme is shown to attain the minimum.