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Networks cardinality estimation using order statistics
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
2015 (English)In: American Control Conference (ACC), 2015: Chicago, IL, 1-3 July 2015,, Piscataway, NJ: IEEE Communications Society, 2015, p. 3810-3817Conference paper, Published paper (Refereed)
Abstract [en]

We consider a network of collaborative peers that aim at distributedly estimating the size of the network they belong to. We assume nodes to be endowed with unique identification numbers (IDs), and we study the performance of size estimators that are based on exchanging these IDs. Motivated by practical scenarios where the time-to-estimate is critical, we specifically address the case where the convergence time of the algorithm, i.e., the number of communications required to achieve the final estimate, is minimal. We thus construct estimators of the network size by exploiting statistical inference concepts on top of the distributed computation of order statistics of the IDs, i.e., of the M biggest IDs available in the network. We then characterize the statistical performance of these estimators from theoretical perspectives and show their effectiveness in practical estimation situations by means of numerical examples.

Place, publisher, year, edition, pages
Piscataway, NJ: IEEE Communications Society, 2015. p. 3810-3817
Series
American Control Conference, ISSN 0743-1619
National Category
Control Engineering
Research subject
Control Engineering; Enabling ICT (AERI); Intelligent industrial processes (AERI)
Identifiers
URN: urn:nbn:se:ltu:diva-32416DOI: 10.1109/ACC.2015.7171924Scopus ID: 2-s2.0-84940941009Local ID: 6e948819-84da-4c91-9255-260d3c9ac8d4ISBN: 978-1-4799-8685-9 (electronic)OAI: oai:DiVA.org:ltu-32416DiVA, id: diva2:1005650
Conference
American Control Conference : 01/07/2015 - 03/07/2015
Note
Validerad; 2016; Nivå 1; 20150327 (damvar)Available from: 2016-09-30 Created: 2016-09-30 Last updated: 2018-07-10Bibliographically 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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