Extremal Properties of Three Dimensional Sensor Networks with Applications
<|reference_start|>Extremal Properties of Three Dimensional Sensor Networks with Applications: 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 $\mathcal{R}$ of volume $V$, how large must the sensing range be to ensure a given degree of coverage of the region to monitor? For a given transmission range, 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.<|reference_end|>
@article{ravelomanana2004extremal,
    title={Extremal Properties of Three Dimensional Sensor Networks with
  Applications},
    author={Vlady Ravelomanana (LIPN)},
    journal={IEEE Transactions on Mobile Computing Vol 3 (2004) pages 246--257},
    year={2004},
    archivePrefix={arXiv},
    eprint={cs/0411027},
    primaryClass={cs.DS cs.DC cs.DM}
}