Optimal topology design for dynamic networks

In this paper, we examine optimization-based methods for designing the network topology when the desired topology should have certain global variational properties, such as minimal power consumption for information exchange links, or supporting fast convergence of consensus-based distributed protocols. We first classify the optimization-based methodology for three distinct categories, namely, for construction of optimal non-geometric networks, time-invariant geometric networks, and time-varying geometric networks. We then proceed to propose optimization-based algorithms for each class of problems that aim to allocate the limited resources, e.g., communication ranges, in the most efficient way while achieving optimal performance. Examples and applications of the developed methodology are also examined.