The notion of a logically routed network was developed to overcome the bottlenecks encountered during the design of a large purely optical network. In the last few years, researchers have proposed the use of torus, Perfect Shuffle, Hypercube,de Bruijn graph, Kautz graph, and Cayley graph as an overlay structure on top of a purely optical network. All these networks have regular structures. Although regular structures have many virtues, it is often difficult in a realistic setting to meet these stringent structural requirements. In this paper, we propose generalized multimesh (GM), a semiregular structure, as an alternate to the proposed architectures. In terms of simplicity of interconnection and routing, this architecture is comparable to the torus network. However, the new architecture exhibits significantly superior topological properties to the torus. For example, whereas a two-dimensional (2-D) torus with N nodes has a diameter of (N0.5), a generalized multimesh network with the same number of nodes and links has a diameter of (N0.25) . In this paper, we also introduce a new metric, flow number, that can be used to evaluate topologies for optical networks. For optical networks, a topology with a smaller flow number is preferable, as it is an indicator of the number of wavelengths necessary for full connectivity. We show that the flow numbers of a 2-D torus, a multimesh, and a de Bruijn network, are (N1.5), (N1.25), and (N log N), respectively, where N is the number of nodes in the network. The advantage of the generalized multimesh over the de Bruijn network lies in the fact that, unlike the de Bruijn network, this network can be constructed for any number of nodes and is incrementally expandable.
Arunabha Sen, Subir Bandyopadhyay, and Bhabani P. Sinha, "A New Architecture and a New Metric for Lightwave Networks," J. Lightwave Technol. 19, 913- (2001)