Abstract
We consider the problem of providing full coverage of a planar region with sensors. Likewise, we consider the connectivity of the sensor network of directional antennas formed by sensors in this region. Suppose that n sensors with coverage angle (also known as beam width) α (n), and reachability radius r(n) are thrown randomly and independently with the uniform distribution in the interior of the unit square. Let p (n) be the probability that a given sensor is active. We prove that if \( p(n) = \Omega \left( \frac{\log (n / r(n)^2 \sin^2 (\alpha (n)/ 4))}{n r(n)^2 \alpha (n) \sin (\alpha (n)/4 )} \right) \) then the probability the sensors provide full coverage of the unit square is at least 1–n − O(1). Likewise, we consider the connectivity of the resulting sensor network. We show that if \(p(n) = \Omega \left( \frac{\log (n / r(n)^2 \sin^2 (\alpha (n) / 4))}{n r(n)^2 \alpha (n) \sin^2 (\alpha (n) /4 )} \right) \) then the probability that a connected subnetwork of sensors provides full coverage is at least 1 – n − O(1).
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Kranakis, E., Krizanc, D., Urrutia, J. (2004). Coverage and Connectivity in Networks with Directional Sensors. In: Danelutto, M., Vanneschi, M., Laforenza, D. (eds) Euro-Par 2004 Parallel Processing. Euro-Par 2004. Lecture Notes in Computer Science, vol 3149. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27866-5_122
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DOI: https://doi.org/10.1007/978-3-540-27866-5_122
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