Think globally, act locally

Abstract

In large-scale resource-constrained systems, such as wireless sensor networks, global objectives should be ideally achieved through inexpensive local interactions. A technique satisfying these requirements is information potentials, in which distributed functions disseminate information about the process monitored by the network. Information potentials are usually computed through local aggregation or gossiping. These methods however, do not consider the topological properties of the network, such as node density, which could be exploited to enhance the performance of the system. This paper proposes a novel aggregation method with which a potential becomes sensitive to the network topology. Our method introduces the notion of affinity spaces, which allow us to uncover the deep connections between the aggregation scope (the radius of the extended neighborhood whose information is aggregated) and the network's Laplacian (which captures the topology of the connectivity graph). Our study provides two additional contributions: (i ) It characterizes the convergence of information potentials for static and dynamic networks. Our analysis captures the impact of key parameters, such as node density, time-varying information, as well as of the addition (or removal) of links and nodes. (ii ) It shows that information potentials are decomposed into wave-like eigenfunctions that depend on the aggregation scope. This result has important implications, for example it prevents greedy routing techniques from getting stuck by eliminating local-maxima. Simulations and experimental evaluation show that our main findings hold under realistic conditions, with unstable links and message loss.