A new architecture and a new metric for lightwave networks

The notion of a logically routed network was developed to overcome the bott lenecks encountered during the design of a large purely optical network. In the last few years, researchers have proposed the use of torus, Perfect Sh uffle, Hypercube, de Bruijn graph, Kautz graph, and Cayley graph as an over lay structure on top of a purely optical network. All these networks have r egular structures. Although regular structures have many virtues, it is oft en difficult in a realistic setting to meet these stringent structural requ irements. In this paper, we propose generalized multimesh (GM), a semiregul ar structure, as an alternate to the proposed architectures. In terms of si mplicity of interconnection and routing, this architecture is comparable to the torus network. However, the new architecture exhibits significantly su perior topological properties to the torus, For example, whereas a two-dime nsional (2-D) torus with N nodes has a diameter of Theta (N-0.5), a general ized multimesh network with the same number of nodes and links has a diamet er of Theta (N-0.25). 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 topol ogy 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 flo w numbers of a 2-D torus, a multimesh, and a de Bruijn network, are Theta ( N-1.5), Theta (N-1.25), and Theta (N log N), respectively, where N is the n umber of nodes in the network. The advantage of the generalized multimesh o ver the de Bruijn network lies in the fact that, unlike the de Bruijn netwo rk, this network can be constructed for any number of nodes and is incremen tally expandable.