A New Architecture and A New Metric for Lightwave Networks

Arunabha Sen

Arizona state university


The notion of logically routed network was developed to overcome the bottlenecks encountered during the design of a large purely optical network. In the last few years the 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 a regular structures. Although the regular structures have many virtues, often times in a realistic setting, it is difficult to meet these stringent structural requirements. In this paper we propose a semi-regular structure, Generalized Multi-Mesh 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 than the torus. For example, whereas a two dimensional torus with N nodes has a diameter of theta(N^0.5) a Multi-Mesh network with the same number of nodes and links has a diameter 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 topology with a small 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 two dimensional torus, a Multi-Mesh and a de Bruijn network are theta(N^1.5), theta(N^1.25) and theta(N log(N)) respectively , where N is the number of nodes in the network. The advantage of the Generalized Multi-Mesh 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]
[Arizona state university]