Connectivity of sparse Bluetooth networks

Consider a random geometric graph defined on n vertices uniformly distributed in 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)/d for some δ> 0, then a constant value of c is sufficient for the graph to be connected, with high probability. It suffices to take c ≥ √ (1 + ɛ)/δ + K for any positive ɛ where K is a constant depending on d only. On the other hand, with c ≤ √ (1 − ɛ)/δ, the graph is disconnected, with high probability. 1 Introduction an

On the Expansion and Diameter of Bluetooth-Like Topologies

The routing capabilities of an interconnection network are strictly related to its bandwidth and latency characteristics, which are in turn quantifiable through the graph-theoretic concepts of expansion and diameter. This paper studies expansion and diameter of a family of subgraphs of the random geometric graph, which closely model the topology induced by the device discovery phase of Bluetooth-based ad hoc networks. The main feature modeled by any such graph, denoted as BT (r(n), c(n)), is the small number c(n) of links that each of the n devices (vertices) may establish with those located within its communi- cation range r(n). First, tight bounds are proved on the expansion of BT (r(n), c(n)) for the whole set of functions r(n) and c(n) for which connectivity has been established in previous works. Then, by leveraging on the expansion result, tight (up to a logarithmic additive term) upper and lower bounds on the diameter of BT (r(n), c(n)) are derived

On the Connectivity of Bluetooth-Based Ad Hoc Networks

We study the connectivity properties of a family of random graphs which closely model the Bluetooth’s device discovery process, where each device tries to connect to other devices within its visibility range in order to establish reliable communication channels yielding a connected topology. Specifically, we provide both analytical and experimental evidence that when the visibility range of each node (i.e., device) is limited to a vanishing function of n, the total number of nodes in the system, full connectivity can still be achieved with high probability by letting each node connect only to a “small” number of visible neighbors. Our results extend previous studies, where connectivity properties were analyzed only for the case of a constant visibility range, and provide evidence that Bluetooth can indeed be used for establishing large ad hoc networks

On the connectivity of bluetooth-based ad hoc networks

Abstract. We study the connectivity properties of a family of random graphs which closely model the Bluetooth’s device discovery process, where each device tries to connect to other devices within its visibility range in order to establish reliable communication channels yielding a connected topology. Specifically, we provide both analytical and experimental evidence that when the visibility range of each node (i.e., device) is limited to a vanishing function of n, the total number of nodes in the system, full connectivity can still be achieved with high probability by letting each node connect only to a “small ” number of visible neighbors. Our results extend previous studies, where connectivity properties were analyzed only for the case of a constant visibility range, and provide evidence that Bluetooth can indeed be used for establishing large ad hoc networks.