Catching elephants with mice

Abstract

We propose a scalably efficient scheme for detecting large-scale physically correlated events in sensor networks. Specifically, we show that in a network of n sensors arbitrarily distributed in the plane, a sample of O (1/ϵ log 1/ϵ) sensor nodes ( mice ) is sufficient to catch any, and only those , events that affect Ω (ϵ n ) nodes ( elephants ), for any 0 < ϵ < 1, as long as the geometry of the event has a bounded Vapnik-Chervonenkis (VC) dimension. In fact, the scheme is provably able to estimate the size of an event within the approximation error of ±ϵ n /4, which can be improved further at the expense of more mice. The detection algorithm itself requires knowledge of the event geometry (e.g., circle, ellipse, or rectangle) for the sake of computational efficiency, but the combinatorial bound on the sample size (set of mice) depends only on the VC, dimension of the event class and not the precise shape geometry. While nearly optimal in theory, due to implicit constant factors, these “scale-free” bounds still prove too large in practice if applied blindly. We therefore propose heuristic improvements and perform empirical parameter tuning to counter the pessimism inherent in these theoretical estimates. Using a variety of data distributions and event geometries, we show through simulations that the final scheme is eminently scalable and practical, say, for n ≥ 1000. The overall simplicity and generality of our technique suggests that it is well suited for a wide class of sensornet applications, including monitoring of physical environments, network anomalies, network security, or any abstract binary event that affects a significant number of nodes in the network.