Critical behavior of blind spots in sensor networks.

Blind spots in sensor networks, i.e., individual nodes or small groups of nodes isolated from the rest of the network, are of great concern as they may significantly degrade the network's ability to collect and process information. As the operations of many types of sensors in realistic applications rely on short-lifetime power supplies (e.g., batteries), once they are used up ("off"), replacements become necessary ("on"). This off-and-on process can lead to blind spots. An issue of both theoretical and practical interest concerns the dynamical process and the critical behavior associated with the occurrence of blind spots. In particular, there can be various network topologies, and the off-and-on process can be characterized by the probability that a node functions normally, or the occupying probability of a node in the network. The question to be addressed in this paper concerns how the dynamics of blind spots depend on the network topology and on the occupying probability. For regular, random, and mixed networks, we provide theoretical formulas relating the probability of blind spots to the occupying probability, from which the critical point for the occurrence of blind spots can be determined. For scale-free networks, we present a procedure to estimate the critical point. While our theoretical and numerical analyses are presented in the framework of sensor networks, we expect our results to be generally applicable to network partitioning issues in other networks, such as the wireless cellular network, the Internet, or transportation networks, where the issue of blind spots may be of concern.