Connectivity of sparse bluetooth networks

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• dc.contributor.author Broutin, Nicolas
• dc.contributor.author Devroye, Luc
• dc.contributor.author Lugosi, Gábor
• dc.date.accessioned 2020-06-08T08:20:23Z
• dc.date.available 2020-06-08T08:20:23Z
• dc.date.issued 2015
• dc.description.abstract Consider a random geometric graph defined on n vertices uniformly distributedin the d-dimensional unit torus. Two vertices are connected if their distance is less than a "visibility radius" rn. We consider Bluetooth networks that are locally sparsified random geometric graphs. Each vertex selects c of its neighbors in the random geometric graph at random and connects only to the selected points. We show that if the visibility radius is at least of the order of n−(1−δ)/dfor some δ>0, then a constant value of c is sufficient forthe graph to be connected, with high probability. It suffices to takec≥(1+ϵ)/δ−−−−−−−√+K for any positive ϵ where Kis a constant depending on d only. On the other hand, with c≤(1−ϵ)/δ−−−−−−−√,the graph is disconnected, with high probability.en
• dc.description.sponsorship GL acknowledges support by the Spanish Ministry of Science and Technology grant MTM2012-37195.
• dc.format.mimetype application/pdf
• dc.identifier.citation Broutin N, Devroye L, Lugosi G. Connectivity of sparse bluetooth networks. Electron Commun Probab. 2015;20(48):1-10. DOI: 10.1214/ECP.v20-3644
• dc.identifier.doi http://dx.doi.org/10.1214/ECP.v20-3644
• dc.identifier.issn 1083-589X
• dc.identifier.uri http://hdl.handle.net/10230/44921
• dc.language.iso eng
• dc.publisher The Institute of Mathematical Statistics and the Bernoulli Society
• dc.relation.ispartof Electronic Communications in Probability. 2015;20(48):1-10
• dc.relation.projectID info:eu-repo/grantAgreement/ES/3PN/MTM2012-37195
• dc.rights This work is licensed under a Creative Commons Attribution 3.0 License.
• dc.rights.accessRights info:eu-repo/semantics/openAccess
• dc.rights.uri https://creativecommons.org/licenses/by/3.0/
• dc.subject.keyword Random geometric graphen
• dc.subject.keyword Connectivityen
• dc.subject.keyword Irrigation graphen
• dc.title Connectivity of sparse bluetooth networksen
• dc.type info:eu-repo/semantics/article
• dc.type.version info:eu-repo/semantics/publishedVersion