Least action routing: Identifying the optimal path in a wireless relay network

Consider a dense wireless network of nodes, which can be used to transfer data between arbitrary sources and destinations. In this paper we develop a methodology based on variational calculus to optimize a number of path metrics, such as the success probability or the total power consumed by a packet delivery in the presence of external interference. We then extend the approach to the case of multiple origin-destination pairs, in which the relaying of each packet causes interference to the other. In both cases, we show that the optimal path may differ significantly from a straight line. We then discuss the consequences of these deviations in the context of network design.