Average Counting via Approximate Histograms

Abstract

We propose a new algorithm for the classical averaging problem for distributed wireless sensors networks. This subject has been studied extensively and there are many clever algorithms in the literature. These algorithms are based on the idea of local exchange of information. They behave well in dense networks (e.g., in networks whose connections form a complete graph), but their convergence to the real average is very slow in linear or cyclic graphs. Our solution is different. In order to calculate the average, we first build an approximate histogram of observed data; then, from this histogram, we estimate the average. In our solution, we use the extreme propagation technique and probabilistic counters. It allows us to find the approximation of the average of a set of measurements done by sensor network with arbitrary precision, controlled by two parameters. Our method requires O(D) rounds, where D is the diameter of the network. We study the message complexity of this algorithm and show that it is of order O(log n) for each node, where n is the size of the network.