Optimal Topology Design of Complex Networks

Given a network, link costs and a maximum cost budget, in this work we apply integer programming techniques to determine the optimal set of links that should be included in the network, in order to provide complex network features. This is accomplished by solving, through branch-and-bound, a mixed integer program based on network flows. We also present a column generation algorithm that, hopefully, will allow us to deal with larger networks. A statistical evaluation of the optimal network topologies found with our methods allowed us to establish a clear relationship between the budget value and a complex network feature (small world, power law degree distribution, for example). In particular, we found that the budget size plays, in our model, a similar role played by the probability of addition or rewiring arcs in stochastic procedures for generating network topologies.