Wavelength Assignment for Directional Hypercube Communications on a Class of WDM Optical Networks

Hypercube communication is one of the most versatile and efficient communication patterns shared by a large number of computational problems. In this paper, we study routing and wavelength assignment for realizing hypercube communications on WDM optical networks including linear arrays and rings with the consideration of communication directions. Specifically, we consider this problem for both bidirectional and unidirectional hypercube communications. For each case, we identify a lower bound on the number of wavelengths required, and present a simple embedding scheme and wavelength assignment algorithm that uses a provably near-optimal number of wavelengths. By realizing hypercube computations in optical networks, the hypercube computation speed can be significantly improved compared with the traditional electronic networks.