Realizing Exchanged Crossed Cube Communication Patterns on Linear Array WDM Optical Networks

The exchanged crossed cube, denoted by ECQ(s, t), is a novel interconnection network with fewer edges and smaller diameter compared to other variations of the corresponding hypercube. The linear array, denoted by L-n, is one of the most popular topologies in optical networks. This paper addresses the routing and wavelength assignment for realizing EC Q (s,t) communication pattern on wavelength division multiplexing (WDM) optical network L-n, where n = s + t + 1. We prove that the congestion for ECQ(s,t) on L-n is equal to 2(s+ t-1) [2(t)/3], which is the lower bound of the minimum number of required wavelengths. In addition, an embedding scheme and an optimal wavelength assignment algorithm that achieve this bound are also proposed.