Toward Resource-Optimal Consensus over the Wireless Medium

TL;DR

This paper analyzes the resource costs of achieving consensus in wireless networks, considering energy, time, and bandwidth, and introduces a new hierarchical averaging scheme that is nearly optimal across these metrics.

Contribution

It provides a comprehensive resource analysis of consensus algorithms in wireless settings and proposes a novel hierarchical averaging method that improves resource efficiency.

Findings

Popular gossip algorithms are energy-efficient but less optimal in time and bandwidth.

Hierarchical averaging is nearly optimal across energy, time, and bandwidth metrics.

Hierarchical averaging offers a favorable tradeoff between resource use and quantization error.

Abstract

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 dominated 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.