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Convergence speed in distributed consensus and averaging
 IN PROC. OF THE 45TH IEEE CDC
, 2006
"... We study the convergence speed of distributed iterative algorithms for the consensus and averaging problems, with emphasis on the latter. We first consider the case of a fixed communication topology. We show that a simple adaptation of a consensus algorithm leads to an averaging algorithm. We prove ..."
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Cited by 138 (4 self)
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We study the convergence speed of distributed iterative algorithms for the consensus and averaging problems, with emphasis on the latter. We first consider the case of a fixed communication topology. We show that a simple adaptation of a consensus algorithm leads to an averaging algorithm. We prove lower bounds on the worstcase convergence time for various classes of linear, timeinvariant, distributed consensus methods, and provide an algorithm that essentially matches those lower bounds. We then consider the case of a timevarying topology, and provide a polynomialtime averaging algorithm.
Gossip algorithms for distributed signal processing
 PROCEEDINGS OF THE IEEE
, 2010
"... Gossip algorithms are attractive for innetwork 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 co ..."
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Cited by 115 (29 self)
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Gossip algorithms are attractive for innetwork 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 paper presents an overview of recent work in the area. We describe convergence rate results, which are related to the number of transmittedmessages 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.
Decentralized Compression and Predistribution via Randomized Gossiping
 in Proc. of the Fifth International Symposium on Information Processing in Sensor Networks (IPSN
, 2006
"... Developing energy efficient strategies for the extraction, transmission, and dissemination of information is a core theme in wireless sensor network research. In this paper we present a novel system for decentralized data compression and predistribution. The system simultaneously computes random pro ..."
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Cited by 81 (17 self)
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Developing energy efficient strategies for the extraction, transmission, and dissemination of information is a core theme in wireless sensor network research. In this paper we present a novel system for decentralized data compression and predistribution. The system simultaneously computes random projections of the sensor data and disseminates them throughout the network using a simple gossiping algorithm. These summary statistics are stored in an efficient manner and can be extracted from a small subset of nodes anywhere in the network. From these measurements one can reconstruct an accurate approximation of the data at all nodes in the network, provided the original data is compressible in a certain sense which need not be known to the nodes ahead of time. The system provides a practical and universal approach to decentralized compression and content distribution in wireless sensor networks. Two example applications, network health monitoring and field estimation, demonstrate the utility of our method.
Geographic gossip: Efficient averaging for sensor networks
 IEEE TRANSACTIONS ON SIGNAL PROCESSING
, 2008
"... Gossip algorithms for distributed computation are attractive due to their simplicity, distributed nature, and robustness in noisy and uncertain environments. However, using standard gossip algorithms can lead to a significant waste of energy by repeatedly recirculating redundant information. For re ..."
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Cited by 64 (6 self)
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Gossip algorithms for distributed computation are attractive due to their simplicity, distributed nature, and robustness in noisy and uncertain environments. However, using standard gossip algorithms can lead to a significant waste of energy by repeatedly recirculating redundant information. For realistic sensor network model topologies like grids and random geometric graphs, the inefficiency of gossip schemes is related to the slow mixing times of random walks on the communication graph. We propose and analyze an alternative gossiping scheme that exploits geographic information. By utilizing geographic routing combined with a simple resampling method, we demonstrate substantial gains over previously proposed gossip protocols. For regular graphs such as the ring or grid, our algorithm improves standard gossip by factors of and, respectively. For the more challenging case of random geometric graphs, our algorithm computes the true average to accuracy using 1 5 1 ( ( log) log) radio transmissions, which yields a log factor improvement over standard gossip algorithms. We illustrate these theoretical results with experimental comparisons between our algorithm and standard methods as applied to various classes of random fields.
Joint SourceChannel Communication for Distributed Estimation in Sensor Networks
"... Power and bandwidth are scarce resources in dense wireless sensor networks and it is widely recognized that joint optimization of the operations of sensing, processing and communication can result in significant savings in the use of network resources. In this paper, a distributed joint sourcechan ..."
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Cited by 51 (3 self)
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Power and bandwidth are scarce resources in dense wireless sensor networks and it is widely recognized that joint optimization of the operations of sensing, processing and communication can result in significant savings in the use of network resources. In this paper, a distributed joint sourcechannel communication architecture is proposed for energyefficient estimation of sensor field data at a distant destination and the corresponding relationships between power, distortion, and latency are analyzed as a function of number of sensor nodes. The approach is applicable to a broad class of sensed signal fields and is based on distributed computation of appropriately chosen projections of sensor data at the destination – phasecoherent transmissions from the sensor nodes enable exploitation of the distributed beamforming gain for energy efficiency. Random projections are used when little or no prior knowledge is available about the signal field. Distinct features of the proposed scheme include: 1) processing and communication are combined into one distributed projection operation; 2) it virtually eliminates the need for innetwork processing and communication; 3) given sufficient prior knowledge about the sensed data, consistent estimation is possible with increasing sensor density even with vanishing total network power; and 4) consistent signal estimation is possible with power and latency requirements growing at most sublinearly with the number of sensor nodes even when little or no prior knowledge about the sensed data is assumed at the sensor nodes.
Gossip along the way: Orderoptimal consensus through randomized path averaging
 IN PROC. 45TH ANNU. ALLERTON CONF. COMMUNICATION, CONTROL, COMPUTING
, 2007
"... 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 adhoc and sensor networks (like grids and random geometric ..."
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Cited by 31 (2 self)
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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 adhoc and sensor networks (like grids and random geometric graphs), the standard nearestneighbor gossip converges very slowly. A recently proposed algorithm called geographic gossip improves gossip efficiency by a p n / log n 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 p n / log n 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.
Hierarchical Spatial Gossip for MultiResolution Representations in Sensor Networks
, 2007
"... In this paper we propose a lightweight algorithm for constructing multiresolution data representations for sensor networks. We compute, at each sensor node u, O(log n) aggregates about exponentially enlarging neighborhoods centered at u. The ith aggregate is the aggregated data among nodes approxim ..."
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Cited by 26 (10 self)
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In this paper we propose a lightweight algorithm for constructing multiresolution data representations for sensor networks. We compute, at each sensor node u, O(log n) aggregates about exponentially enlarging neighborhoods centered at u. The ith aggregate is the aggregated data among nodes approximately within 2 i hops of u. We present a scheme, named the hierarchical spatial gossip algorithm, to extract and construct these aggregates, for all sensors simultaneously, with a total communication cost of O(npolylog n). The hierarchical gossip algorithm adopts atomic communication steps with each node choosing to exchange information with a node distance d away with probability 1/d 3. The attractiveness of the algorithm attributes to its simplicity, low communication cost, distributed nature and robustness to node failures and link failures. Besides the natural applications of multiresolution data summaries in data validation and information mining, we also demonstrate the application of the precomputed spatial multiresolution data summaries in answering range queries efficiently.
Weighted gossip: distributed averaging using nondoubly stochastic matrices
 In Proceedings of the 2010 IEEE International Symposium on Information Theory
, 2010
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Shape Segmentation and Applications in Sensor Networks
"... Abstract—Many sensor network protocols in the literature implicitly assume that sensor nodes are deployed uniformly inside a simple geometric region. When the real deployment deviates from that, we often observe degraded performance. It is desirable to have a generic approach to handle a sensor fiel ..."
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Cited by 21 (3 self)
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Abstract—Many sensor network protocols in the literature implicitly assume that sensor nodes are deployed uniformly inside a simple geometric region. When the real deployment deviates from that, we often observe degraded performance. It is desirable to have a generic approach to handle a sensor field with complex shape. In this paper, we propose a segmentation algorithm that partitions an irregular sensor field into nicely shaped pieces such that algorithms and protocols that assume a nice sensor field can be applied inside each piece. Across the segments, problem dependent structures specify how the segments and data collected in these segments are integrated. This unified topologyadaptive spatial partitioning would benefit many settings that currently assume a nicely shaped sensor field. Our segmentation algorithm does not require sensor locations and only uses network connectivity information. Each node is given a ‘flow direction ’ that directs away from the network boundary. A node with no flow direction becomes a sink, and attracts other nodes in the same segment. We evaluate the performance improvements by integrating shape segmentation with applications such as distributed indices and random sampling. I.
Which distributed averaging algorithm should I choose for my sensor network
 Proc. 27th IEEE Conf. Computer Communications and Networks
, 2008
"... Average consensus and gossip algorithms have recently received significant attention, mainly because they constitute simple and robust algorithms for distributed information processing over networks. Inspired by heat diffusion, they compute the average of sensor networks measurements by iterating lo ..."
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Cited by 21 (2 self)
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Average consensus and gossip algorithms have recently received significant attention, mainly because they constitute simple and robust algorithms for distributed information processing over networks. Inspired by heat diffusion, they compute the average of sensor networks measurements by iterating local averages until a desired level of convergence. Confronted with the diversity of these algorithms, the engineer may be puzzled in his choice for one of them. As an answer to his/her need, we develop precise mathematical metrics, easy to use in practice, to characterize the convergence speed and the cost (time, message passing, energy...) of each of the algorithms. In contrast to other works focusing on timeinvariant scenarios, we evaluate these metrics for ergodic timevarying networks. Our study is based on Oseledec’s theorem, which gives an almostsure description of the convergence speed of the algorithms of interest. We further provide upper bounds on the convergence speed. Finally, we use these tools to make some experimental observations illustrating the behavior of the convergence speed with respect to network topology and reliability in both average consensus and gossip algorithms. A. Problem statement. I.