# A New Architecture and A New Metric for Lightwave Networks

##
Arunabha Sen

### Arizona state university

### Résumé:

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.