Toward Resource-Optimal Consensus Over the Wireless Medium

We carry out a comprehensive study of the resource cost of averaging consensus in wireless networks. Most previous approaches suppose a graphical network, which abstracts away crucial features of the wireless medium, and measure resource consumption only in terms of the total number of transmissions required to achieve consensus. Under a path-loss model, we study the resource requirements of consensus with respect to three wireless-appropriate metrics: total transmit energy, elapsed time, and time-bandwidth product. First, we characterize the performance of several popular gossip algorithms, showing that they may be order-optimal with respect to transmit energy but are strictly suboptimal with respect to elapsed time and time-bandwidth product. Further, we propose a new consensus scheme, termed hierarchical averaging, and show that it is nearly order-optimal with respect to all three metrics. Finally, we examine the effects of quantization, showing that hierarchical averaging provides a nearly order-optimal tradeoff between resource consumption and quantization error.