Routing and wavelength assignment for 3-ary n-cube in array-based optical network

The k-ary n  -cube, denoted Qnk, is one of the popular communication patterns of parallel algorithms. This paper addresses the routing and wavelength assignment for Qn3 communication pattern in array-based WDM optical network. By using congestion estimation and giving a routing and wavelength assignment strategy, we prove that the optimal number of wavelengths is n3−13n−1.

► In this paper, we considered Qn3,b communication pattern and Lnb optical network. ► Firstly, we obtained the congestion of embedding Qn3 into LnLn. ► With the help of it, we proved the optimal number of wavelengths required was n3−13n−1. ► Then routing and wavelength assignment strategy was designed. ► The strategy satisfied the required number of wavelengths was optimal.