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A tight bound on the Bernoulli trials network size estimator
Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.ORCID iD: 0000-0002-7443-8174
Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.ORCID iD: 0000-0002-4310-7938
Number of Authors: 22016 (English)In: 2016 IEEE 55th Conference on Decision and Control, CDC 2016, Piscataway, NJ: Institute of Electrical and Electronics Engineers (IEEE), 2016, p. 3474-3480, article id 7798790Conference paper, Published paper (Refereed)
Abstract [en]

We consider the problem of finding exact statistical characterizations of the Bernoulli trials network size estimator, a simple algorithm for distributedly counting the number of agents in an anonymous communication network for which the probability of committing estimation errors scales down exponentially with the amount of information exchanged by the agents. The estimator works by cascading a local, randomized, voting step (i.e., the i.i.d. generation of some Bernoulli trials) with an average consensus on these votes. We derive a tight upper bound on the probability that this strategy leads to an incorrect estimate, and refine the offline procedure for selecting the Bernoulli trials success rate.

Place, publisher, year, edition, pages
Piscataway, NJ: Institute of Electrical and Electronics Engineers (IEEE), 2016. p. 3474-3480, article id 7798790
Series
IEEE Conference on Decision and Control, E-ISSN 0743-1546
National Category
Control Engineering
Research subject
Control Engineering
Identifiers
URN: urn:nbn:se:ltu:diva-37510DOI: 10.1109/CDC.2016.7798790ISI: 000400048103103Scopus ID: 2-s2.0-85010720911Local ID: b90d2ca1-9f38-48bc-b98a-6e0211ccf71fISBN: 9781509018376 (electronic)OAI: oai:DiVA.org:ltu-37510DiVA, id: diva2:1011008
Conference
55th IEEE Conference on Decision and Control, CDC 2016, Las Vegas, United States, 12-14 December 2016
Available from: 2016-10-03 Created: 2016-10-03 Last updated: 2017-12-18Bibliographically approved
In thesis
1. Distributed Estimation of Network Cardinalities
Open this publication in new window or tab >>Distributed Estimation of Network Cardinalities
2017 (English)Licentiate thesis, comprehensive summary (Other academic)
Alternative title[sv]
Distribuerad skattning av nätverkskardinalitet
Abstract [en]

In distributed applications knowing the topological properties of the underlying communication network may lead to better performing algorithms. For instance, in distributed regression frameworks, knowing the number of active sensors allows to correctly weight prior information against evidence in the data. Moreover, continuously estimating the number of active nodes or communication links corresponds to monitoring the network connectivity and thus to being able to trigger network reconfiguration strategies. It is then meaningful to seek for estimators of the properties of the communication graphs that sense these properties with the smallest possible computational/communications overheads.

Here we consider the problem of distributedly counting the number of agents in a network. This is at the same time a prototypical summation problem and an essential task instrumental to evaluating more complex algebraic expressions such as products and averages which are in turn useful in many distributed control, optimization and estimation problems such as least squares, sensor calibration, vehicle coordination and Kalman filtering.

Being interested in generality, we consider computations in anonymous networks, i.e., in frameworks where agents are not ensured to have unique IDs and the network lacks a centralized authority. This setting implies that the set of distributedly computable functions is limited, that there is no size estimation algorithm with uniformly bounded computational complexity that can provide correct estimates with probability one, and thus that scalable size estimators are non-deterministic functions of the true network size. Natural questions are then: which one is the scheme that leads to topology estimators that are optimal in Mean Squared Error (MSE) terms? And what are the fundamental limitations of information aggregation for topology estimation purposes, i.e., what can be estimated and what not?

Our focus is then to understand how to distributedly estimate cardinalities given devices with bounded resources (e.g., battery/energy constraints, communication bandwidth, etc.) and how considering different assumptions and trade-offs leads to different optimal strategies. We specifically consider the case of peer-to-peer networks where all the participants are required to: i) share the same final result (and thus the same view of the network) and ii) keep the communication and computational complexity at each node uniformly bounded in time.

To this aim, we study four different estimation strategies that consider different tradeoffs between accuracy and convergence speed and characterize their statistical performance in terms of bias and MSE.

Place, publisher, year, edition, pages
Luleå: Luleå University of Technology, 2017
Series
Licentiate thesis / Luleå University of Technology, ISSN 1402-1757
National Category
Control Engineering
Research subject
Control Engineering
Identifiers
urn:nbn:se:ltu:diva-62460 (URN)978-91-7583-843-4 (ISBN)978-91-7583-844-1 (ISBN)
Presentation
2017-05-17, A1545, Luleå, 13:00
Available from: 2017-03-15 Created: 2017-03-13 Last updated: 2017-12-18Bibliographically approved

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Lucchese, RiccardoVaragnolo, Damiano

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