Routing and wavelength assignment for 3-ary n-cube communication patterns in linear array optical networks for n communication rounds

•In this paper, we considered Qn3,b communication patterns and Lnb optical networks.•All packets are transmitted one dimension after another.•Embedding scheme ϕ was designed and the congestion about dimensions under ϕ was obtained.•The optimal number of wavelengths under ϕ was achieved.•An optimal routing and wavelength assignment strategy was designed.

k-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 3-ary n-cube communication patterns on a bidirectional linear array WDM optical networks when the information is transmitted one dimension after another. By giving an embedding scheme ϕ, we prove the optimal number of wavelengths under ϕ and design a routing and wavelength assignment strategy of it.