  Existing works on distributed consensus explore linear iterations based on
reversible Markov chains, which contribute to the slow convergence of the
algorithms. It has been observed that by overcoming the diffusive behavior of
reversible chains, certain nonreversible chains lifted from reversible ones mix
substantially faster than the original chains. In this paper, we investigate
the idea of accelerating distributed consensus via lifting Markov chains, and
propose a class of Location-Aided Distributed Averaging (LADA) algorithms for
wireless networks, where nodes' coarse location information is used to
construct nonreversible chains that facilitate distributed computing and
cooperative processing. First, two general pseudo-algorithms are presented to
illustrate the notion of distributed averaging through chain-lifting. These
pseudo-algorithms are then respectively instantiated through one LADA algorithm
on grid networks, and one on general wireless networks. For a $k\times k$ grid
network, the proposed LADA algorithm achieves an $\epsilon$-averaging time of
$O(k\log(\epsilon^{-1}))$. Based on this algorithm, in a wireless network with
transmission range $r$, an $\epsilon$-averaging time of
$O(r^{-1}\log(\epsilon^{-1}))$ can be attained through a centralized algorithm.
Subsequently, we present a fully-distributed LADA algorithm for wireless
networks, which utilizes only the direction information of neighbors to
construct nonreversible chains. It is shown that this distributed LADA
algorithm achieves the same scaling law in averaging time as the centralized
scheme. Finally, we propose a cluster-based LADA (C-LADA) algorithm, which,
requiring no central coordination, provides the additional benefit of reduced
message complexity compared with the distributed LADA algorithm.
