Realizing the ternary n-cube communication pattern on a ring-connected WDM optical network

The k-ary n-cube, denoted Qnk, turns out to be a popular communication pattern for parallel processing. This paper focuses on the issue of efficiently executing a parallel algorithm with bidirectional/unidirectional ternary n-cube communication pattern on a ring-connected WDM optical network. For either of these two communication patterns, a routing scheme is suggested, and the corresponding wavelength assignment strategy is presented. For the bidirectional communication, the number of wavelengths required by the proposed embedding scheme is shown to attain the minimum. We conjecture that the congestion of the embedding Qn3 in C3n is minimal regardless of the embedding scheme.