Location-Aided Fast Distributed Averaging

Existing works on distributed averaging explore linear iterations based on reversible Markov chains, and hence the convergence is bounded to be slow due to the diffusive behavior of the reversible random walk. In this paper, we study the possibility of utilizing nonreversible chains to achieve faster averaging in wireless networks. We first show that it is possible to achieve an -averaging time of ¿(r-1 log(1/)) in a wireless network with a transmission radius r, with a centralized grid-based algorithm. We then proceed to propose a purely distributed algorithm, the Location-Aided Distributed Averaging-Uniform (LADA-U) algorithm, where the direction information of neighbors is used to construct nonreversible chains with uniform stationary distributions. It is shown that LADA-U can achieve the same scaling law in averaging time as the centralized scheme, but needs a substantially larger transmission range than minimum connectivity requirement, mainly due to the induced diffusive behavior.