On the Connectivity of Bluetooth-Based Ad Hoc Networks

Crescenzi, Pierluigi; Nocentini, Carlo; Pietracaprina, Andrea; Pucci, Geppino; Sandri, Carlo

doi:10.1007/978-3-540-74466-5_103

Cited by 4 publications

(7 citation statements)

References 7 publications

(10 reference statements)

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“…Arguably the most interesting values for r n are those just above the connectivity threshold for the underlying graph

G_{n} (r_{n})

, that is, when r n is proportional to

\sqrt[d]{\log n / n}

. The results of Crescenzi et al show that for such values of r n , connectivity of

S_{n} (r_{n}, c_{n})

is guaranteed, with high probability, when c n is a sufficiently large constant multiple of

\log n

. In this paper we show that this bound can be improved substantially.…”

Section: Introductionmentioning

confidence: 66%

“…The graph

S_{n} = S_{n} (r_{n}, c_{n})

was introduced in the context of the Bluetooth network , and is sometimes called the Bluetooth or scatternet graph with parameters

n, r_{n}

, and c n . The model was introduced and studied in .…”

Section: Introductionmentioning

confidence: 99%

“…The case when r n is small is a more delicate issue, since the geometry now plays a crucial role. Crescenzi, Nocentini, Pietracaprina, and Pucci proved that in dimension d = 2 there exist constants

γ_{1}, γ_{2}

such that if

r_{n} \geq γ_{1} \sqrt{\log n / n}

and

c_{n} \geq γ_{2} \log (1 / r_{n})

, then

S_{n} (r_{n}, c_{n})

is connected with high probability.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Connectivity threshold of Bluetooth graphs

Broutin

Devroye

Fraiman

et al. 2012

Random Struct. Alg.

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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.

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“…Arguably the most interesting values for r n are those just above the connectivity threshold for the underlying graph

G_{n} (r_{n})

, that is, when r n is proportional to

\sqrt[d]{\log n / n}

. The results of Crescenzi et al show that for such values of r n , connectivity of

S_{n} (r_{n}, c_{n})

is guaranteed, with high probability, when c n is a sufficiently large constant multiple of

\log n

. In this paper we show that this bound can be improved substantially.…”

Section: Introductionmentioning

confidence: 66%

“…The graph

S_{n} = S_{n} (r_{n}, c_{n})

was introduced in the context of the Bluetooth network , and is sometimes called the Bluetooth or scatternet graph with parameters

n, r_{n}

, and c n . The model was introduced and studied in .…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Connectivity threshold of Bluetooth graphs

Broutin

Devroye

Fraiman

et al. 2012

Random Struct. Alg.

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show abstract

“…Later, Crescenzi et al [2009] showed that full connectivity is achieved even when r goes to zero as n increases.…”

Section: Introductionmentioning

confidence: 97%

Expansion properties of (secure) wireless networks

Panconesi

Radhakrishnan

2012

ACM Trans. Algorithms

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“…The following random graph model for the Bluetooth topology has been proposed in [4] and subsequently generalized in [5]. The devices are represented by n nodes, whose coordinates are randomly chosen within the unit square [0, 1] 2 ; each node selects c(n) neighbors among all visible nodes, that is, among all nodes within Euclidean distance r(n), where r(n) models the visibility range, which is assumed to be the same for all devices.…”

Section: Introductionmentioning

confidence: 99%

On the Expansion and Diameter of Bluetooth-Like Topologies

2012

Self Cite

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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 communication 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, nearly-tight upper and lower bounds on the diameter of BT(r(n),c(n)) are derived. In particular, we show asymptotically tight bounds on the diameter when the communication range is near the minimum needed for connectivity, the typical scenario considered in practical applications

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On the Connectivity of Bluetooth-Based Ad Hoc Networks

Cited by 4 publications

References 7 publications

Connectivity threshold of Bluetooth graphs

Connectivity threshold of Bluetooth graphs

Expansion properties of (secure) wireless networks

On the Expansion and Diameter of Bluetooth-Like Topologies

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