Fundamentals of Large Sensor Networks: Connectivity, Capacity, Clocks, and Computation

Sensor networks potentially feature large numbers of nodes. The nodes can monitor and sense their environment over time, communicate with each other over a wireless network, and process information that they exchange with each other. They differ from data networks in that the network as a whole may be designed for a specific application. We study the theoretical foundations of such large-scale sensor networks. We address four fundamental organizational and operational issues related to large sensor networks: connectivity, capacity, clocks, and function computation. To begin with, a sensor network must be connected so that information can indeed be exchanged between nodes. The connectivity graph of an ad hoc network is modeled as a random graph and the critical range for asymptotic connectivity is determined, as well as the critical number of neighbors that a node needs to connect to. Next, given connectivity, we address the issue of how much data can be transported over the sensor network. We present fundamental bounds on capacity under several models, as well as architectural implications for how wireless communication should be organized. Temporal information is important both for the applications of sensor networks as well as their operation. We present fundamental bounds on the synchronizability of clocks in networks, and also present and analyze algorithms for clock synchronization. Finally, we turn to the issue of gathering relevant information, which sensor networks are designed to do. One needs to study optimal strategies for in-network aggregation of data, in order to reliably compute a composite function of sensor measurements, as well as the complexity of doing so. We address the issue of how such computation can be performed efficiently in a sensor network and the algorithms for doing so, for some classes of functions.