Fault Tolerance of Optical Hypercube Interconnection Networks with r -Communication Pattern

Abstract

As power grids and optical interconnection networks are interdependent, the reliabilities of the optical networks are critical issues in power systems. The optical networks hold prominent performance including wide bandwidth, low loss, strong anti-interference capability, high fidelity, and reliable performance. They are regarded as promising alternatives to electrical networks for parallel processing. This paper is aimed at taking the first step in understanding the communication efficiencies of optical networks. For that purpose, on optical networks, we propose a series of novel notions including communication pattern, $r$ -communication graph, reduced diameter, enhanced connectivity, $r$ -diameter, and $r$ -connectivity. Using these notions, we determine that the $r$ -diameter and $r$ -connectivity of the optical $n$ -dimensional hypercube network are $⌈n/r⌉$ and $\left(\begin{array}{c}n\\ 1\end{array}\right)+\left(\begin{array}{c}n\\ 2\end{array}\right)+\cdots +\left(\begin{array}{c}n\\ r\end{array}\right)$ , respectively. Since the parameter $r$ is variable, we can adjust different values of $r$ on the basis of the wavelength resources and load of the optical networks, achieving enhanced communication efficiencies of these networks. Compared with the electric $n$ -dimensional hypercube network, the proposed communication pattern on the optical hypercube network not only reduces the maximum communication delay of the conventional electrical hypercube significantly but also improves its fault tolerance remarkably.