2011/03/02 by Nicolas Broutin, Broutin, Nicolas, Luc Devroye +5
Computer Science · Mathematics · #05C80 #60C05 #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Networking and Internet Architecture (cs.NI) #Probability (math.PR) #cs.DM #cs.NI #math.CO #math.PR #msc:05C80 #msc:60C05
paper · pdf · doi:10.48550/arxiv.1103.0351
21 pages, 5 figures
arxiv created 2011/03/02 · arxiv updated 2011/03/03
We study the connectivity properties of random Bluetooth graphs that model certain "ad hoc" wireless networks. The graphs are obtained as "irrigation subgraphs" of the well-known random geometric graph model. There are two parameters that control the model: the radius r that determines the "visible neighbors" of each node and the number of edges c that each node is allowed to send to these. The randomness comes from the underlying distribution of data points in space and from the choices of each vertex. We prove that no connectivity can take place with high probability for a range of parameters r, c and completely characterize the connectivity threshold (in c) for values of r close the critical value for connectivity in the underlying random geometric graph.