Distributed Demand-aware Network Design using Bounded Square Root of Graphs.

While the traditional design of network topologies is demand oblivious, recent advances in reconfigurable networks enable real-time and dynamic communication network topologies, e.g., in datacenter networks. This trend motivates a new paradigm where topologies can adjust to the demand they need to serve. We consider the static and distributed version of this network design problem where the input is a request distribution, $\mathcal{D}$ (demand matrix), and a bound Δ, on the maximum degree of the output topology. In turn, the objective is to design an (undirected) demand-aware network N of bounded-degree Δ, which minimizes the expected path length (with respect to $\mathcal{D}$).This paper draws a connection between the k-root of graphs and the network design problem and uses forest-decomposition of the demand matrix as the primary methodology. In turn, we provide new algorithms for demand-aware network design, including cases where our algorithms are (order) optimal and improve previous results. In addition, we provide, for the first time and for the case of bounded arboricity, (i) an efficient distributed algorithm for the CONGEST model and (ii) an efficient and PRAM-based parallel algorithm. We also present empirical results on real-world demand matrices where our algorithms produce both low-degree and low-expected path length network designs.