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.Comment: 33 pages, 4 figure