A criterion for cost optimal construction of irregular networks

In recent years, we have seen an increased interest in irregular network topologies. This has been spawned by the introduction of switches with flexible forwarding capabilities, and routing methods for irregular networks. This paper provides a simple mechanism for cost optimal construction of irregular networks based on three criterions: (1) Distributing the nodes over the switches in such a way that the resulting link utilisation is balanced (when assuming a uniform traffic distribution); (2) using as small number of switches as possible; (3) using the smallest possible switches. This is assuming no parallel links as these will add additional ports to the switch without helping the connectivity. Assuming switch scalability up to a certain limit, our construction gives cost optimal network topologies up to this limit. This provides insight into the influence of the switch size on network cost. Beyond the limitation in switch size we indicate strategies for further scalability that may also be used for the case of having only fixed sized switches.