Embedding Hypercube Communications on Optical Chordal Ring Networks

Hypercube communication is one of the most versatile and efficient communication patterns for parallel computation. Routing and wavelength assignments for realizing hypercube communications on WDM linear arrays, rings, meshes and tori have been discussed in our past researches. In this paper, we study routing and wavelength assignment for realizing hypercube communications on WDM chordal ring networks of degree 3. We design embedding scheme and derive the number of wavelengths required for different chord length. Based on embedding scheme of double cycle embedding, we also provide the analysis of chord length with optimal number of wavelengths to realize hypercube communications on 3-degree chordal rings. Results show that the wavelength requirement for realizing hypercube communications on optical networks has been further reduced on optical 3-degree chordal ring networks compared with some topologies discussed before. Our results have both theoretical and practical significance as WDM optical networks have an increasing popularity