Routing and wavelength assignment for exchanged crossed cubes on ring-topology optical networks

Abstract

The exchanged crossed cube, denoted by $$\textit{ECQ}(s, t)$$ , is a novel graph with fewer edges and smaller diameter compared to other variations of the corresponding hypercube. The ring topology, denoted by $$R_n$$ , is one of the most popular topologies in Wavelength division multiplexing optical networks. This paper addresses the routing and wavelength assignment problem for realizing $$\textit{ECQ}(s, t)$$ communication pattern on $$R_n$$ , where $$n=s+t+1$$ . We propose an embedding scheme. Base on the embedding scheme, a wavelength assignment algorithm using $$2^{s+t-2}+\lfloor 2^t/3\rfloor $$ wavelengths is devised. We show that the wavelength assignment algorithm uses no more than 1.25 times of wavelengths compared to the optimal wavelength number, i.e., it is a factor 1.25 approximation algorithm. Moreover, the number of additional required wavelengths is no more than $$\lfloor 2^{t-1}/3\rfloor $$ .