10,728 research outputs found
Gossip along the way: order-optimal consensus through randomized path averaging
Gossip algorithms have recently received significant attention, mainly because they constitute simple and robust algorithms for distributed information processing over networks. However for many topologies that are realistic for wireless ad-hoc and sensor networks (like grids and random geometric graphs), the standard nearest-neighbor gossip converges very slowly. A recently proposed algorithm called geographic gossip improves gossip efficiency by a factor for random geometric graphs, by exploiting geographic information of node locations. In this paper we prove that a variation of geographic gossip that averages along routed paths, improves efficiency by an additional factor and is order optimal for grids and random geometric graphs. Our analysis provides some general techniques and can be used to provide bounds on the performance of randomized message passing algorithms operating over various graph topologies
Gossip Algorithms for Distributed Signal Processing
Gossip algorithms are attractive for in-network processing in sensor networks
because they do not require any specialized routing, there is no bottleneck or
single point of failure, and they are robust to unreliable wireless network
conditions. Recently, there has been a surge of activity in the computer
science, control, signal processing, and information theory communities,
developing faster and more robust gossip algorithms and deriving theoretical
performance guarantees. This article presents an overview of recent work in the
area. We describe convergence rate results, which are related to the number of
transmitted messages and thus the amount of energy consumed in the network for
gossiping. We discuss issues related to gossiping over wireless links,
including the effects of quantization and noise, and we illustrate the use of
gossip algorithms for canonical signal processing tasks including distributed
estimation, source localization, and compression.Comment: Submitted to Proceedings of the IEEE, 29 page
Ergodic Randomized Algorithms and Dynamics over Networks
Algorithms and dynamics over networks often involve randomization, and
randomization may result in oscillating dynamics which fail to converge in a
deterministic sense. In this paper, we observe this undesired feature in three
applications, in which the dynamics is the randomized asynchronous counterpart
of a well-behaved synchronous one. These three applications are network
localization, PageRank computation, and opinion dynamics. Motivated by their
formal similarity, we show the following general fact, under the assumptions of
independence across time and linearities of the updates: if the expected
dynamics is stable and converges to the same limit of the original synchronous
dynamics, then the oscillations are ergodic and the desired limit can be
locally recovered via time-averaging.Comment: 11 pages; submitted for publication. revised version with fixed
technical flaw and updated reference
Location-Aided Fast Distributed Consensus in Wireless Networks
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 grid
network, the proposed LADA algorithm achieves an -averaging time of
. Based on this algorithm, in a wireless network with
transmission range , an -averaging time of
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.Comment: 44 pages, 14 figures. Submitted to IEEE Transactions on Information
Theor
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