On the asymptotic connectivity of random networks under the random connection model

Mao, G; Anderson, BD

On the asymptotic connectivity of random networks under the random connection model

Mao, G

Anderson, BD

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Publication Type:: Conference Proceeding
Citation:: Proceedings - IEEE INFOCOM, 2011, pp. 631 - 639
Issue Date:: 2011-08-02

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Field	Value	Language
dc.contributor.author	Mao, G https://orcid.org/0000-0002-3598-4949	en_US
dc.contributor.author	Anderson, BD	en_US
dc.date.issued	2011-08-02	en_US
dc.identifier.citation	Proceedings - IEEE INFOCOM, 2011, pp. 631 - 639	en_US
dc.identifier.isbn	9781424499212	en_US
dc.identifier.issn	0743-166X	en_US
dc.identifier.uri	http://hdl.handle.net/10453/32920
dc.description.abstract	Consider a network where all nodes are distributed on a unit square following a Poisson distribution with known density ρand a pair of nodes separated by an Euclidean distance x are directly connected with probability g(x/rρ ), where g : [0,∞ρ+b/cp) [0,1] satisfies three conditions: rotational invariance, qnon-increasing monotonicity and integral boundedness, √ρ+b/Cp = ∫R2g(∥x∥)dx and bis a constant, independent of the event that another pair of nodes are directly connected. In this paper, we analyze the asymptotic distribution of the number of isolated nodes in the above network using the Chen-Stein technique and the impact of the boundary effect on the number of isolated nodes as ρ. On that basis we derive a necessary condition for the above network to be asymptotically almost surely connected. These results form an important link in expanding recent results on the connectivity of the random geometric graphs from the commonly used unit disk model to the more generic and more practical random connection model. © 2011 IEEE.	en_US
dc.relation.ispartof	Proceedings - IEEE INFOCOM	en_US
dc.relation.isbasedon	10.1109/INFCOM.2011.5935242	en_US
dc.title	On the asymptotic connectivity of random networks under the random connection model	en_US
dc.type	Conference Proceeding
utslib.for	1005 Communications Technologies	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Electrical and Data Engineering
pubs.organisational-group	/University of Technology Sydney/Strength - CRIN - Realtime Information Networks
utslib.copyright.status	closed_access
pubs.publication-status	Published	en_US

Abstract:

Consider a network where all nodes are distributed on a unit square following a Poisson distribution with known density ρand a pair of nodes separated by an Euclidean distance x are directly connected with probability g(x/rρ ), where g : [0,∞ρ+b/cp) [0,1] satisfies three conditions: rotational invariance, qnon-increasing monotonicity and integral boundedness, √ρ+b/Cp = ∫R2g(∥x∥)dx and bis a constant, independent of the event that another pair of nodes are directly connected. In this paper, we analyze the asymptotic distribution of the number of isolated nodes in the above network using the Chen-Stein technique and the impact of the boundary effect on the number of isolated nodes as ρ. On that basis we derive a necessary condition for the above network to be asymptotically almost surely connected. These results form an important link in expanding recent results on the connectivity of the random geometric graphs from the commonly used unit disk model to the more generic and more practical random connection model. © 2011 IEEE.

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http://hdl.handle.net/10453/32920