Robust computation of aggregates in wireless sensor networks: distributed randomized algorithms and analysis

A wireless sensor network consists of a large number of small, resource-constrained devices and usually operates in hostile environments that are prone to link and node failures. Computing aggregates such as average, minimum, maximum and sum is fundamental to various primitive functions of a sensor network like system monitoring, data querying, and collaborative information processing. In this paper we present and analyze a suite of randomized distributed algorithms to efficiently and robustly compute aggregates. Our Distributed Random Grouping (DRG) algorithm is simple and natural and uses probabilistic grouping to progressively converge to the aggregate value. DRG is local and randomized and is naturally robust against dynamic topology changes from link/node failures. Although our algorithm is natural and simple, it is nontrivial to show that it converges to the correct aggregate value and to bound the time needed for convergence. Our analysis uses the eigen-structure of the underlying graph in a novel way to show convergence and to bound the running time of our algorithms. We also present simulation results of our algorithm and compare its performance to various other known distributed algorithms. Simulations show that DRG needs much less transmissions than other distributed localized schemes, namely gossip and broadcast flooding.