## Geographic Gossip: Efficient Aggregation for Sensor Networks (2006)

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Venue: | in Proc. Information Processing in Sensor Networks (IPSN |

Citations: | 89 - 4 self |

### BibTeX

@INPROCEEDINGS{Dimakis06geographicgossip:,

author = {Alexandros G. Dimakis},

title = {Geographic Gossip: Efficient Aggregation for Sensor Networks},

booktitle = {in Proc. Information Processing in Sensor Networks (IPSN},

year = {2006},

pages = {69--76},

publisher = {ACM Press}

}

### Years of Citing Articles

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### Abstract

Gossip algorithms for aggregation have recently received significant attention for sensor network applications because of their simplicity and robustness in noisy and uncertain environments. However, gossip algorithms can waste significant energy by essentially passing around redundant information multiple times. For realistic sensor network model topologies like grids and random geometric graphs, the inefficiency of gossip schemes is caused by slow mixing times of random walks on those graphs. We propose and analyze an alternative gossiping scheme that exploits geographic information. By utilizing a simple resampling method, we can demonstrate substantial gains over previously proposed gossip protocols. In particular, for random geometric graphs, our algorithm computes the true average to accuracy 1/n a using O(n 1.5 √ log n) radio transmissions, which reduces the energy consumption by a algorithms. q n factor over standard gossip log n

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Citation Context ...se technical results. In Section 4, we experimentally evaluate the performance of our algorithm. 2. PROPOSED ALGORITHM AND MAIN RESULTS 2.1 Problem statement 2.1.1 Graph model Following previous work =-=[4,8]-=-, we model our wireless sensor network as a random geometric graph [17]. In this model, denoted G(n, r), the n sensor locations are chosen uniformly and independently in the unit square, and each pair... |

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Citation Context ...ll the nodes in each square are connected with each other. Proof. The proof of part (a) following easily since it requires Θ(n log n) balls thrown randomly to cover n bins with high probability. (See =-=[16]-=- and [7] for more details). Moreover, if we select r(n) = √ 5α(n), then simple geometric calculations show that each node will be able to communicate to all other nodes in its square, as well as all n... |

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Citation Context ...ess networks. We leverage the fact that sensors nodes typically know their locations, and can therefore use this knowledge to perform geographic routing. Localization is a well studied problem (e.g., =-=[13, 20]-=-), since geographic knowledge is required in numerous applications. With this perspective ins0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Figure 1: Illustration of a random ... |

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Citation Context ... only been proven for regular graphs, and it is unclear whether their algorithm will prove efficient for the networks in this paper. In [15], the authors use an algorithm based on Flajolet and Martin =-=[6]-=- to compute averages and bound the averaging time in terms of a “spreading time” associated with the communication graph. However, they only show the optimality of their algorithm for a graph consisti... |

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Citation Context ... The key issue is how many iterations it takes for such gossip algorithm to converge to a sufficiently accurate estimate. Variations of this problem have received significant attention in recent work =-=[4,5,11,12]-=-. The convergence speed of a nearest-neighbor gossip algorithm, known as the averaging time, turns out to be closely linked to the mixing time of the Markov chain defined by a weighted random walk on ... |

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Citation Context ...ess networks. We leverage the fact that sensors nodes typically know their locations, and can therefore use this knowledge to perform geographic routing. Localization is a well studied problem (e.g., =-=[13, 20]-=-), since geographic knowledge is required in numerous applications. With this perspective ins0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Figure 1: Illustration of a random ... |

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Citation Context ... The key issue is how many iterations it takes for such gossip algorithm to converge to a sufficiently accurate estimate. Variations of this problem have received significant attention in recent work =-=[4,5,11,12]-=-. The convergence speed of a nearest-neighbor gossip algorithm, known as the averaging time, turns out to be closely linked to the mixing time of the Markov chain defined by a weighted random walk on ... |

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Citation Context ...an some transmission radius r. (As discussed in Section 5, our results have natural analogs for lattices, and other graph structures that are reasonable models of wireless networks). It is well known =-=[7, 8, 17]-=- that in order to have good connectivity and minimize interference, the transmission radius r(n) has to q log n scale like Θ( ). For our analysis, we assume that comn munication within this transmissi... |

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Citation Context ... The key issue is how many iterations it takes for such gossip algorithm to converge to a sufficiently accurate estimate. Variations of this problem have received significant attention in recent work =-=[4,5,11,12]-=-. The convergence speed of a nearest-neighbor gossip algorithm, known as the averaging time, turns out to be closely linked to the mixing time of the Markov chain defined by a weighted random walk on ... |

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Citation Context ...average in a completely distributed manner. Although fairly simple, the distributed averaging problem and related consensus problems can be viewed as building blocks for solving more complex problems =-=[19, 21]-=-, including computing general linear functions as well as optimization of non-linear functions in sensor networks. The key issue is how many iterations it takes for such gossip algorithm to converge t... |

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Citation Context ...nsmissions for ɛ = Θ(n −a ). Therefore, our proposed algorithm saves a factor of q n log n in communication energy by exploiting geographic information. Two very recent papers by Moallemi and Van Roy =-=[14]-=- and Mosk-Aoyama and Shah [15] also consider the problem of computing averages in networks. The consensus propagation algorithm of [14] is a modified form of belief propagation that attempts to mitiga... |

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Citation Context ...typical wireless sensor networks, even an optimized gossip algorithm can result in very high energy consumption. For example, a common model for an wireless sensor network is a random geometric graph =-=[17]-=-, in which all nodes communicate with neighbors within a radius r. With the transmission radius scaling in the standard way as r(n) = Θ( q log n n ), even an optimized gossip algorithm requires Θ(n 2 ... |

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Citation Context ...n) = Θ( ), greedy routing always reaches the closest n q n node v to the random target in O( ) radio transmislog n sions. Note that in practice more sophisticated geographic routing algorithms (e.g., =-=[10]-=-) can be used to ensure that the packet approaches the random target when there are “holes” in the node density. However, greedy geographic routing is good enough for our model and other choices for r... |

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Citation Context ...o in order to bound the averaging time Tave(n, ɛ), we apply rejection sampling in order to temper the distribution. In particular, we apply the following rejection sampling scheme, due to Bash et al. =-=[2]-=-. Let �a be an n-vector of areas of the sensors’ Voronoi regions. We set a threshold τ on the cell areas. Sensors with cell area smaller than τ always accept a query, and sensors with cell areas large... |

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Citation Context ...average in a completely distributed manner. Although fairly simple, the distributed averaging problem and related consensus problems can be viewed as building blocks for solving more complex problems =-=[19, 21]-=-, including computing general linear functions as well as optimization of non-linear functions in sensor networks. The key issue is how many iterations it takes for such gossip algorithm to converge t... |

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(Show Context)
Citation Context ...E(n, ɛ) = O √ log ɛ log n −1 « . (8) Moreover, note that if we set ɛ = 1/n α in equation (8), then we obtain E(n, 1/n α “ ) = O n 3/2√ ” log n . 2.3 Related work and Comparisons In a series of papers =-=[3, 4]-=-, Boyd et al. have analyzed the performance of standard gossip algorithms. Their fastest standard gossip algorithm for the ensemble of random geometric graphs G(n, r) has a ɛ-averaging time [4] 1 Tave... |

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Citation Context ...ndom routing. The proposed algorithm can be used instead of nearest neighbor gossip in all the schemes that use consensus based aggregation and will greatly reduce the communication cost. For example =-=[18, 19, 21]-=- use similar ideas for localization, Kalman filtering and sensor fusion. In these schemes, geographic gossip can be used instead of standard nearestneighbor gossip to improve energy consumption. Ackno... |

14 |
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Citation Context ...aph. However, they only show the optimality of their algorithm for a graph consisting of a single cycle, so it is currently difficult to speculate how it would perform on a geometric random graph. In =-=[1]-=- the authors consider the related problem of computing the average of a network in a single node. They propose 1 This quantity is computed in section IV.A of [4] but the result is expressed in terms o... |

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12 | Information dissemination via gossip: Applications to averaging and coding
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(Show Context)
Citation Context ...herefore, our proposed algorithm saves a factor of q n log n in communication energy by exploiting geographic information. Two very recent papers by Moallemi and Van Roy [14] and Mosk-Aoyama and Shah =-=[15]-=- also consider the problem of computing averages in networks. The consensus propagation algorithm of [14] is a modified form of belief propagation that attempts to mitigate the inefficiencies introduc... |