Low Mean Internodal Distance Network Topologies Through Simulated Annealing.

Using simulated annealing, networks have been found with mean internodal distances lower than any previously reported for a given number of nodes N with a maximum of p outgoing links per node. Thus, these networks form the closest known approximations to Moore networks. However, the improvements in mean internodal distance obtained are relatively small (a few percent) and this improvement decreases rapidly with increasing p. A more important (at least in the p=2 case) by-product of the simulated annealing process is its seeming promotion of uniformity (over individual nodes) in mean distance to the rest of the network. This side-effect of the annealing process is useful in that it promotes "access fairness" over the network nodes even when the properties of the initial network are grossly unfair. Furthermore, this result suggests that an annealing approach might be useful when a given network attribute must be made uniform over the network nodes.