Broutin, NicolasDevroye, LucLugosi, Gábor2020-06-082020-06-082015Broutin N, Devroye L, Lugosi G. Connectivity of sparse bluetooth networks. Electron Commun Probab. 2015;20(48):1-10. DOI: 10.1214/ECP.v20-36441083-589Xhttp://hdl.handle.net/10230/44921Consider 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.application/pdfengThis work is licensed under a Creative Commons Attribution 3.0 License.info:eu-repo/semantics/articlehttp://dx.doi.org/10.1214/ECP.v20-3644Random geometric graphConnectivityIrrigation graphinfo:eu-repo/semantics/openAccess