Controlled Hopwise Averaging: Bandwidth/Energy-Efficient Asynchronous Distributed Averaging for Wireless Networks

TL;DR

This paper introduces Controlled Hopwise Averaging (CHA), an asynchronous distributed algorithm for wireless network averaging that significantly improves bandwidth and energy efficiency by optimizing iteration control and exploiting broadcast capabilities.

Contribution

The paper proposes CHA, a novel asynchronous averaging algorithm that enhances efficiency through broadcast exploitation and decentralized control, outperforming existing methods in convergence speed and transmission reduction.

Findings

CHA outperforms Pairwise Averaging in convergence rate.

CHA requires fewer transmissions to achieve averaging.

Simulation results confirm CHA's superior efficiency on random geometric graphs.

Abstract

This paper addresses the problem of averaging numbers across a wireless network from an important, but largely neglected, viewpoint: bandwidth/energy efficiency. We show that existing distributed averaging schemes have several drawbacks and are inefficient, producing networked dynamical systems that evolve with wasteful communications. Motivated by this, we develop Controlled Hopwise Averaging (CHA), a distributed asynchronous algorithm that attempts to "make the most" out of each iteration by fully exploiting the broadcast nature of wireless medium and enabling control of when to initiate an iteration. We show that CHA admits a common quadratic Lyapunov function for analysis, derive bounds on its exponential convergence rate, and show that they outperform the convergence rate of Pairwise Averaging for some common graphs. We also introduce a new way to apply Lyapunov stability theory, using the Lyapunov function to perform greedy, decentralized, feedback iteration control. Finally, through extensive simulation on random geometric graphs, we show that CHA is substantially more efficient than several existing schemes, requiring far fewer transmissions to complete an averaging task.