Random channel assignment in the plane

McDiarmid, Colin

doi:10.1002/rsa.10077

Cited by 40 publications

(58 citation statements)

References 31 publications

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“…For sake of simplicity, let us suppose that this value of k is an integer. By (38) of Corollary 4, with high probability there is Θ(ln n) nodes inside the sphere of radius V 1/3 /2k. Consider now two adjacent sub-cubes as depicted in the figure below :…”

Section: Hop-diametermentioning

confidence: 91%

Extremal properties of three-dimensional sensor networks with applications

Ravelomanana

2004

IEEE Trans. on Mobile Comput.

149

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In this paper, we analyze various critical transmitting/sensing ranges for connectivity and coverage in three-dimensional sensor networks. As in other large-scale complex systems, many global parameters of sensor networks undergo phase transitions: For a given property of the network, there is a critical threshold, corresponding to the minimum amount of the communication effort or power expenditure by individual nodes, above (resp. below) which the property exists with high (resp. a low) probability.For sensor networks, properties of interest include simple and multiple degrees of connectivity/coverage. First, we investigate the network topology according to the region of deployment, the number of deployed sensors and their transmitting/sensing ranges. More specifically, we consider the following problems:Assume that n nodes, each capable of sensing events within a radius of r, are randomly and uniformly distributed in a 3-dimensional region R of volume V , how large must the sensing range r Sense be to ensure a given degree of coverage of the region to monitor? For a given transmission range r Trans , what is the minimum (resp. maximum) degree of the network? What is then the typical hop-diameter of the underlying network? Next, we show how these results affect algorithmic aspects of the network by designing specific distributed protocols for sensor networks.

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Section: Hop-diametermentioning

confidence: 91%

Extremal properties of three-dimensional sensor networks with applications

Ravelomanana

2004

IEEE Trans. on Mobile Comput.

149

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“…It can be observed that the transmitting power P x has no effect in the evaluation of Equation 25 for determining the occurrence of a collision, but it only affects the interrogation range. With the considered values of antenna gains and interrogation range in Table 1, we set the transmitting power to 30 dBm in order to make sure that the conventional RFID tags can be energized at 5 m.…”

Section: Methodsmentioning

confidence: 99%

“…This model [25] assumes that the readers are equipped with an omnidirectional antenna: their signal propagates in the same way along all the directions. Due to the path loss, there is a specific distance d beyond which the signal http://jes.eurasipjournals.com/content/2013/1/10 emitted by a reader is not powerful enough to feed the circuitry of a tag.…”

Section: Disk Graph Modelmentioning

confidence: 99%

Trade-off between maximum cardinality of collision sets and accuracy of RFID reader-to-reader collision detection

et al. 2013

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As the adoption of the radio-frequency identification (RFID) technology is increasing, many applications require a dense reader deployment. In such environments, reader-to-reader interference becomes a critical problem, so the proposal of effective anti-collision algorithms and their analysis are particularly important. Existing reader-to-reader anti-collision algorithms are typically analyzed using single interference models that consider only direct collisions. The additive interference models, which consider the sum of interferences, are more accurate but require more computational effort. The goal of this paper is to find the difference in accuracy between single and additive interference models and how many interference components should be considered in additive models. An in-depth analysis evaluates to which extent the number of the additive components in a possible collision affects the accuracy of collision detection. The results of the investigation shows that an analysis limited to direct collisions cannot reach a satisfactory accuracy, but the collisions generated by the addition of the interferences from a large number of readers do not affect significantly the detection of RFID reader-to-reader collisions.

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“…e.g. [9], [13], [16], [17], [22], [23]. We particularly mention the work of the Hipercom Project, e.g.…”

Section: Introductionmentioning

confidence: 99%

The Expected Size of the Rule k Dominating Set

2006

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Dai, Li, and Wu proposed Rule k, a localized approximation algorithm that attempts to find a small connected dominating set in a graph. Here we consider the "average case"performance of Rule k for the model of random unit disk graphs constructed from n random points in an ℓn × ℓn square. If k ≥ 3 and ℓn = o( √ n), then the expected size of the Rule k dominating set is Θ(ℓ 2 n ) as n → ∞. If ℓn ≤ n 10 log n , then expected size of the minimum CDS is also Θ(ℓ 2 n ).

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Random channel assignment in the plane

Cited by 40 publications

References 31 publications

Extremal properties of three-dimensional sensor networks with applications

Extremal properties of three-dimensional sensor networks with applications

Trade-off between maximum cardinality of collision sets and accuracy of RFID reader-to-reader collision detection

The Expected Size of the Rule k Dominating Set

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