Implementing Exchanged Hypercube Communication Patterns on Ring-Connected WDM Optical Networks

Abstract

The exchanged hypercube, denoted by EH(s,t), is a graph obtained by systematically removing edges from the corresponding hypercube, while preserving many of the hypercube's attractive properties. Moreover, ring-connected topology is one of the most promising topologies in Wavelength Division Multiplexing (WDM) optical networks. Let R_n denote a ring-connected topology. In this paper, we address the routing and wavelength assignment problem for implementing the EH(s,t) communication pattern on R_n, where n=s+t+1. We design an embedding scheme. Based on the embedding scheme, a near-optimal wavelength assignment algorithm using 2^s+t-2+⌊2^t/3⌋ wavelengths is proposed. We also show that the wavelength assignment algorithm uses no more than an additional 25 percent of (or ⌊2^t-1/3⌋) wavelengths, compared to the optimal wavelength assignment algorithm.