Abstract
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.