J. Whitbeck and M. Dias de Amorim and V. Conan and J.-L. Guillaume

While a natural fit for modeling and understanding mobile networks, time-varying graphs remain poorly understood. Indeed, many of the usual concepts of static graphs have no obvious counterpart in time-varying ones. In this paper, we introduce the notion of temporal reachability graphs. A (tau, sigma)-reachability graph is a time-varying directed graph derived from an existing connectivity graph. An edge exists from one node to another in the reachability graph at time t if there exists a journey (i.e., a spatiotemporal path) in the connectivity graph from the first node to the second, leaving after t, with a positive edge traversal time tau, and arriving within a maximum delay sigma. We make three contributions. First, we develop the theoretical framework around temporal reachability graphs. Second, we harness our theoretical findings to propose an algorithm for their efficient computation. Finally, we demonstrate the analytic power of the temporal reachability graph concept by applying it to synthetic and real-life data sets. On top of defining clear upper bounds on communication capabilities, reachability graphs highlight asymmetric communication opportunities and offloading potential.

J. Whitbeck and M. Dias de Amorim and V. Conan and J.-L. Guillaume