Average Counting via Approximate Histograms -- Preliminary Report

In this paper, we propose a novel method of solving the averaging problem for distributed Wireless Sensors Networks. This method is based on approximated histograms of measurements made by a sensor network. Our method uses a set of probabilistic counters and allows to find the approximation of the average of a set of measures done by sensor network with arbitrary, controlled by two parameters, precision. The exchange of information is based on broadcasting method exploiting extreme propagation technique. Our method require O(D) rounds, where D is the diameter of the network. We analyze both kind of errors which occurs in our method: discretization errors caused by the histogram representation of the data and errors due to the probabilistic nature of the used counters.