Geodesic
Multilevel Regular Coverings of the Plane by Discs
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 14 (2014) no. 1, pp. 112-128

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In this paper, the problem of the least dense regular covering the plane with disks of different radii is discussed. The author generalizes different types of regular coverings and introduces a new one, the “multilevel” covering. The bounds for these coverings densities are obtained and a three-level covering with density $\approx 1.083$ is proposed.
Keywords: covering the plane by discs, wireless sensor networks. 
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     author = {I. I. Takhonov},
     title = {Multilevel {Regular} {Coverings} of the {Plane} by {Discs}},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {112--128},
     publisher = {mathdoc},
     volume = {14},
     number = {1},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2014_14_1_a8/}
}
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I. I. Takhonov. Multilevel Regular Coverings of the Plane by Discs. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 14 (2014) no. 1, pp. 112-128. http://geodesic.mathdoc.fr/item/VNGU_2014_14_1_a8/