Hierarchical averaging over wireless sensor networks

We introduce an approach to gossip algorithms that exploits three aspects of the wireless medium: superposition, broadcast, and power control. Instead of sending pairwise messages between neighbors on a fixed network topology, we construct gossip algorithms in which nodes can simultaneously recover multiple neighbors´ messages and in which nodes can adjust the set of their neighbors by adjusting transmit power. We present two averaging algorithms, each based on a hierarchical clustering of the network. In the first algorithm, clusters of nodes transmit their estimates locally and randomly select a representative node for communications at the next level. In the second, each cluster mutually averages and then cooperatively transmits at the next level. For path-loss environments, these schemes achieve order-optimal or near order-optimal performance.