Geodesic
The Coverage of a Planar Region by Randomly Deployed Sensors
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 10 (2010) no. 4, pp. 7-25

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The problem of energy-efficient monitoring of a planar region by sensors with adjustable sensing ranges can be reduced to the problem of constructing least density coverage of the area by disks of various (not known a priori) radii. Due to the complexity of the problem, only so-called regular covers that use disks of one, two or three radii are usually considered. In that case centers of disks are placed in nodes of a grid formed by regular polygons and in some interior points of the polygons. However, for many applications it is unrealistic to expect all sensors to be placed exactly in the prescribed positions. Assuming that the sensors are randomly deployed, we propose close to regular covers and explore relationship among achievable coverage quality, node density, and sensor network lifetime.
Keywords: sensor networks, coverage density, random distribution. 
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     author = {T. A. Aldyn-ool and A. I. Erzin and V. V. Zalyubovskiy},
     title = {The {Coverage} of a {Planar} {Region} by {Randomly} {Deployed} {Sensors}},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
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     publisher = {mathdoc},
     volume = {10},
     number = {4},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2010_10_4_a1/}
}
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T. A. Aldyn-ool; A. I. Erzin; V. V. Zalyubovskiy. The Coverage of a Planar Region by Randomly Deployed Sensors. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 10 (2010) no. 4, pp. 7-25. http://geodesic.mathdoc.fr/item/VNGU_2010_10_4_a1/