On distributed data aggregation and the precision of approximate histograms

We consider selected aspects of distributed data aggregation in wireless sensor networks (WSNs), including random sampling, averaging, and the construction of histograms. We propose a novel algorithm for distributed random sampling based on the extrema propagation technique. We also consider the problem of construction of approximate histograms in WSNs and estimation of the average of sensory data and bin counts using these histograms. We present the results of theoretical analysis of the precision of estimators calculated from approximate histograms and propose a modification of the original method which allows for construction of approximate equi-depth histograms based on a random sample from data. The theoretical and experimental results show that the estimates calculated from approximate equi-depth histograms are more precise than those obtained using equi-width histograms. We also present an idea of an algorithm for a distributed variant of the Count Distinct problem, which uses the extrema propagation technique.