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## Gossip-Based Computation of Aggregate Information (2003)

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Citations: | 472 - 2 self |

### Citations

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Citation Context ...ing quantiles as that of actually finding the φ-largest element, with probability at least 1 − δ. Our algorithm is essentially a decentralized implementation of the simple randomized “Find” al=-=gorithm [25]-=-. It starts with the entire (multi-)set of elements, and in each round chooses a pivot element from among the remaining elements uniformly at random. The algorithm then counts the number of elements l... |

2075 | Pastry: Scalable, distributed object location and routing for large-scale peer-to-peer systems
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Citation Context ...d computation to highly distributed systems. For example, large-scale peer-to-peer (P2P) networks with millions of servers are being used or designed for distributed information storage and retrieval =-=[9, 30, 32], an-=-d advances in hardware are leading to the augmentation of ∗ Supported by an NSF Graduate Research Fellowship † Supported by NSF Grants IIS-0133481 and CCR-0205452, and by gifts from Microsoft and ... |

1386 | Tag: a tiny aggregation service for ad-hoc sensor networks. The fifth symposium on Operating systems design and implementation
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Citation Context ...† Supported by NSF Grants IIS-0133481 and CCR-0205452, and by gifts from Microsoft and Intel. 1 our physical environment with sensor networks consisting of hundreds of thousands of small sensor node=-=s [24, 28, 35]-=-. Applications for such large-scale distributed systems have three salient properties that distinguish them from traditional centralized or small-scale distributed systems. First, the dynamics of larg... |

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Citation Context ...d computation to highly distributed systems. For example, large-scale peer-to-peer (P2P) networks with millions of servers are being used or designed for distributed information storage and retrieval =-=[9, 30, 32], an-=-d advances in hardware are leading to the augmentation of ∗ Supported by an NSF Graduate Research Fellowship † Supported by NSF Grants IIS-0133481 and CCR-0205452, and by gifts from Microsoft and ... |

964 |
Wireless Integrated Network Sensors
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Citation Context ...† Supported by NSF Grants IIS-0133481 and CCR-0205452, and by gifts from Microsoft and Intel. 1 our physical environment with sensor networks consisting of hundreds of thousands of small sensor node=-=s [24, 28, 35]-=-. Applications for such large-scale distributed systems have three salient properties that distinguish them from traditional centralized or small-scale distributed systems. First, the dynamics of larg... |

882 |
Epidemic algorithms for replicated database maintenance
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Citation Context ...de contacts one or a few nodes in each round (usually chosen at random), and exchanges information with these nodes. The dynamics of information spread bear a resemblance to the spread of an epidemic =-=[5, 10], an-=-d lead to high faulttolerance and “self-stabilization” [8, 10, 34]. Gossip-based protocols usually do not require error recovery mechanisms, and thus enjoy a large advantage in simplicity, while o... |

845 | The space complexity of approximating the frequency moments
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- 1999
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Citation Context ...design protocols for several more complex types of queries. Specifically, we show how to extend the analysis in a relatively straightforward way to answer many kinds of aggregate queries in databases =-=[3, 4, 11, 13, 14, 15, 33]-=-, essentially any query that can be approximated well using linear synopses. A somewhat more elaborate analysis shows that using only small messages and few rounds of the underlying communication mech... |

540 | Reversible Markov Chains and Random Walks on Graphs. Book in preparation
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Citation Context ...by A. Theorem 2.6 allows us to leverage a large body of literature on the convergence speed of Markov Chains and Random Walks for the analysis of our aggregate computation protocols (see for instance =-=[1, 23, 31]).-=- In particular, whenever the underlying network is an expander, then we obtain diffusion speed T (n, ε) = O(log n + log 1 ε ). Several Peer-to-Peer topologies explicitly generate expander graphs [22... |

444 | Probabilistic counting algorithms for data base applications
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Citation Context ...design protocols for several more complex types of queries. Specifically, we show how to extend the analysis in a relatively straightforward way to answer many kinds of aggregate queries in databases =-=[3, 4, 11, 13, 14, 15, 33]-=-, essentially any query that can be approximated well using linear synopses. A somewhat more elaborate analysis shows that using only small messages and few rounds of the underlying communication mech... |

407 | Random Walks on Graphs: a Survey
- Lovasz
- 1993
(Show Context)
Citation Context ...by A. Theorem 2.6 allows us to leverage a large body of literature on the convergence speed of Markov Chains and Random Walks for the analysis of our aggregate computation protocols (see for instance =-=[1, 23, 31]).-=- In particular, whenever the underlying network is an expander, then we obtain diffusion speed T (n, ε) = O(log n + log 1 ε ). Several Peer-to-Peer topologies explicitly generate expander graphs [22... |

384 | The Mathematical Theory of Infectious Diseases and its Applications. - Bailey - 1975 |

330 |
A survey of gossiping and broadcasting in communication networks.
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Citation Context ...lue originating with any one node diffuses through the network. This notion is made precise in Section 2, although we hasten to add here that it does not in general coincide with the “broadcast time=-=” [6, 18, 29]��-=-� the time it takes to disseminate a message to all nodes using point-to-point communication. Push-Sum is generic with respect to the underlying mechanism for communication, and its convergence speed ... |

324 | Stable distributions, pseudorandom generators, embeddings and data stream computation.
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Citation Context ...i-way joins in databases. • Approximate histogram construction using sketches [33]. • Lp-norms, by using either range-summable hash functions with limited independence [13], or p-stable distributi=-=ons [19]. -=-• Distinct Value Queries, using hash functions [14, 4]. 4. Random Sampling and Quantiles A second important task besides computing sums and averages is to find random samples and quantiles of a mult... |

287 | Randomized rumor spreading.
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Citation Context ...pproximation algorithms for the (NP-complete) problem of optimal broadcasting. Karp et al. consider tradeoffs between the number of rounds of gossip and the number of message duplicates that are sent =-=[20]-=-. The impact of message size restrictions on the ability to solve distributed computation tasks is investigated in [21]. It is shown that for the problems of locating the closest copy 3 of a resource ... |

245 |
A fast and simple randomized parallel algorithm for the maximal independent set problem.
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Citation Context ...btain linearity), all nodes have to use the same multipliers ξu. Alon et al. show how to generate fourwise independent multipliers from a random seed of length logarithmic in the size of the universe=-= [2, 4]-=-, so it suffices to disseminate this seed to all nodes i. 8 4.1. Random Sampling In order to draw a random sample from M, each node i first samples an element q0,i from Mi uniformly at random 4 , and ... |

186 | Processing complex aggregate queries over data streams.
- Dobra, Gehrke, et al.
- 2002
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Citation Context ...design protocols for several more complex types of queries. Specifically, we show how to extend the analysis in a relatively straightforward way to answer many kinds of aggregate queries in databases =-=[3, 4, 11, 13, 14, 15, 33]-=-, essentially any query that can be approximated well using linear synopses. A somewhat more elaborate analysis shows that using only small messages and few rounds of the underlying communication mech... |

172 |
On spreading a rumor,”
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Citation Context .... The dissemination time of gossip distributions, and the time to broadcast one value to all nodes, has been studied in the past, see [18] for a survey. In particular, Frieze and Grimmett, and Pittel =-=[16, 27]-=- give precise constants in the O(log n) upper bound for Uniform Gossip. Feige et al. [12] consider random broadcasting on random graphs and hypercubes. Ravi [29] and Bar-Noy et al. [6] study approxima... |

123 | Tracking join and self-join sizes in limited storage.
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Citation Context |

122 | Building low-diameter P2P networks,
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(Show Context)
Citation Context ...31]). In particular, whenever the underlying network is an expander, then we obtain diffusion speed T (n, ε) = O(log n + log 1 ε ). Several Peer-to-Peer topologies explicitly generate expander graph=-=s [22, 26]-=-, and others [30, 32, 36] build hypercube-like networks which are expected to also have good expansion. Thus, we believe that our techniques will yield quick convergence on many P2P architectures. 2.4... |

102 | The shortest path problem for graphs with random arc-lengths.
- Frieze, Grimmett
- 1985
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Citation Context .... The dissemination time of gossip distributions, and the time to broadcast one value to all nodes, has been studied in the past, see [18] for a survey. In particular, Frieze and Grimmett, and Pittel =-=[16, 27]-=- give precise constants in the O(log n) upper bound for Uniform Gossip. Feige et al. [12] consider random broadcasting on random graphs and hypercubes. Ravi [29] and Bar-Noy et al. [6] study approxima... |

94 |
Lectures on finite Markov chains.
- Saloff-Coste
- 1996
(Show Context)
Citation Context ...v Chain so defined is actually ergodic.sMarkov Chain is reversible, i.e. πiαi,j = πjαj,i, for all i, j, these two distance measures can be related in the following precise sense (see Lemma 2.4.6 f=-=rom [31], and its analogue for di-=-screte time Markov Chains): Lemma 2.5 [31] If A defines a reversible Markov Chain, then whenever maxj� eT j ·At π − 1�2,π ≤ δ, we have maxj� eT j ·A2t π − 1�∞ ≤ δ2 . Hence, by... |

88 | Scalable faulttolerant aggregation in large process groups.
- Gupta, Renesse, et al.
- 2001
(Show Context)
Citation Context ...ption. Third, due to the large scale of the system, the values ofsaggregate functions over the data in the whole network (or a large part of it) are often more important than individual data at nodes =-=[17, 24, 34]-=-. For example, in a sensor network with temperature sensors, we are often more interested in the average or median temperature measured by all sensors in an area rather than the single measurement at ... |

79 | Estimating aggregates on a peer-to-peer network
- Bawa, Garcia-Molina, et al.
- 2003
(Show Context)
Citation Context ...ues (such as sums, averages, quantiles, etc.) in a decentralized and fault-tolerant fashion, while using small messages only. The Node Aggregation problem was recently defined formally by Bawa et al. =-=[7], who re-=-strict their attention to sums, averages, minima, and maxima. They define several natural notions of “validity” of a result in the presence of node failures, and show that “practical validity”... |

70 | Protocols and impossibility results for gossip-based communication mechanisms.
- Kempe, Kleinberg
- 2002
(Show Context)
Citation Context ...he number of rounds of gossip and the number of message duplicates that are sent [20]. The impact of message size restrictions on the ability to solve distributed computation tasks is investigated in =-=[21]-=-. It is shown that for the problems of locating the closest copy 3 of a resource or building an approximate minimum spanning tree, different gossip distributions exhibit qualitatively different behavi... |

56 |
Rapid rumor ramification: Approximating the minimum broadcast time. In:
- Ravi
- 1994
(Show Context)
Citation Context ...lue originating with any one node diffuses through the network. This notion is made precise in Section 2, although we hasten to add here that it does not in general coincide with the “broadcast time=-=” [6, 18, 29]��-=-� the time it takes to disseminate a message to all nodes using point-to-point communication. Push-Sum is generic with respect to the underlying mechanism for communication, and its convergence speed ... |

55 | Message multicasting in heterogeneous networks.
- Bar-Noy, Guha, et al.
- 2000
(Show Context)
Citation Context ...lue originating with any one node diffuses through the network. This notion is made precise in Section 2, although we hasten to add here that it does not in general coincide with the “broadcast time=-=” [6, 18, 29]��-=-� the time it takes to disseminate a message to all nodes using point-to-point communication. Push-Sum is generic with respect to the underlying mechanism for communication, and its convergence speed ... |

54 | An approximate L 1 -difference algorithm for massive data streams
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Citation Context |

38 |
Randomized broadcast in networks. Random Structures and Algorithms 1 447–460. 50 [Gr] [HR
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Citation Context ...nodes, has been studied in the past, see [18] for a survey. In particular, Frieze and Grimmett, and Pittel [16, 27] give precise constants in the O(log n) upper bound for Uniform Gossip. Feige et al. =-=[12]-=- consider random broadcasting on random graphs and hypercubes. Ravi [29] and Bar-Noy et al. [6] study approximation algorithms for the (NP-complete) problem of optimal broadcasting. Karp et al. consid... |

14 | An approximate L p difference algorithm for massive data streams
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4 |
pressure: Distributed recovery from attacks in peer-to-peer systems
- Peer
- 2002
(Show Context)
Citation Context ...31]). In particular, whenever the underlying network is an expander, then we obtain diffusion speed T (n, ε) = O(log n + log 1 ε ). Several Peer-to-Peer topologies explicitly generate expander graph=-=s [22, 26]-=-, and others [30, 32, 36] build hypercube-like networks which are expected to also have good expansion. Thus, we believe that our techniques will yield quick convergence on many P2P architectures. 2.4... |