Two-phase cardinality estimation protocols for sensor networks with provable precision

Cichoń, Jacek; Lemiesz, Jakub; Szpankowski, Wojciech; Zawada, Marcin

doi:10.1109/wcnc.2012.6214120

Cited by 18 publications

(10 citation statements)

References 9 publications

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“…Considering a certain agent i, the set of p We notice that estimator (11) has strong similarities with the size estimators proposed in [26], [27], [28].…”

Section: B Estimator Based On Max Consensusmentioning

confidence: 96%

Fast distributed estimation of empirical mass functions over anonymous networks

Terelius

Varagnolo

Baquero

et al. 2013

52nd IEEE Conference on Decision and Control

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Fast distributed estimation of empirical mass functions over anonymous networks. Abstract-The aggregation and estimation of values over networks is fundamental for distributed applications, such as wireless sensor networks. Estimating the average, minimal and maximal values has already been extensively studied in the literature. In this paper, we focus on estimating empirical distributions of values in a network with anonymous agents. In particular, we compare two different estimation strategies in terms of their convergence speed, accuracy and communication costs. The first strategy is deterministic and based on the average consensus protocol, while the second strategy is probabilistic and based on the max consensus protocol.

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“…Considering a certain agent i, the set of p We notice that estimator (11) has strong similarities with the size estimators proposed in [26], [27], [28].…”

Section: B Estimator Based On Max Consensusmentioning

confidence: 96%

Fast distributed estimation of empirical mass functions over anonymous networks

Terelius

Varagnolo

Baquero

et al. 2013

52nd IEEE Conference on Decision and Control

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“…Most of them are based on discrete random variables: e.g. maximum of geometric random variables is used in Probabilistic Counting [12] and HyperLogLog [11], the balls-andbins model in Linear Counting [29] and Bernoulli trials in Two-Phase Algorithm [5]. A few algorithms based on continuous random variables have been proposed as well: Minima and Optimal Counting [16,4] and COMP [21] use order statistics of the uniform and exponential distribution.…”

Section: Related Workmentioning

confidence: 99%

“…Building on these solutions several distributed size estimation protocols dedicated to wireless systems have been proposed recently (e.g., [3,5,6,7,19,20]). However, these protocols implicitly assume that a communication framework is already established and hide the complexity of the underlying implementation.…”

Section: Related Workmentioning

confidence: 99%

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On Distributed Cardinality Estimation: Random Arcs Recycled

Kardas

Kutyłowski

Lemiesz

2014

2015 Proceedings of the Twelfth Workshop on Analytic Algorithmics and Combinatorics (ANALCO)

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We introduce and analyze a distributed cardinality estimation algorithm for a network consisted of not synchronized nodes. Our solution can be regarded as a generalization of the classic approximate counting algorithm based on the balls and bins model and is connected to the well studied process of covering the circle with random arcs. Although the algorithm is presented in the context of a radio network, the basic idea is applicable to any system in which many uncoordinated nodes communicate over a shared medium. In the paper we prove the correctness of the algorithm and by the methods of complex analysis we carefully examine the accuracy and precision of the estimator we have proposed. We also show that the construction of the proposed algorithm is a backbone for simple distributed summation.

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“…Let us note that in [4] during an analysis of some distributed algorithm for Ad Hoc networks a formula…”

Section: Introductionmentioning

confidence: 99%

On Delta-Method of Moments and Probabilistic Sums

Cichoń

Gołębiewski

Kardas

et al. 2013

2013 Proceedings of the Tenth Workshop on Analytic Algorithmics and Combinatorics (ANALCO)

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We discuss a general framework for determining asymptotics of the expected value of random variables of the form f (X) in terms of a function f and central moments of the random variable X. This method may be used for approximation of entropy, inverse moments, and some statistics of discrete random variables useful in analysis of some randomized algorithms. Our approach is based on some variant of the Delta Method of Moments. We formulate a general result for an arbitrary distribution and next we show its specic extension to random variables which are sums of identically distributed independent random variables. Our method simplies previous proofs of results of several authors and can be automated to a large extent. We apply our method to the binomial, negative binomial, Poisson and hypergeometric distribution. We extend the class of functions for which our method is applicable to some subclass of exponential functions and double exponential functions for some cases.

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Two-phase cardinality estimation protocols for sensor networks with provable precision

Cited by 18 publications

References 9 publications

Fast distributed estimation of empirical mass functions over anonymous networks

Fast distributed estimation of empirical mass functions over anonymous networks

On Distributed Cardinality Estimation: Random Arcs Recycled

On Delta-Method of Moments and Probabilistic Sums

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