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Covering a planar region by randomly distributed sensors. (Russian. English summary) Zbl 1249.68002

Summary: 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 region 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, the centers of the 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 the relationship among achievable coverage quality, node density, and sensor network lifetime.

MSC:

68M10 Network design and communication in computer systems
05B40 Combinatorial aspects of packing and covering
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