Geodesic
On the number and arrangement of sensors for~the~multiple covering of bounded plane~domains
Diskretnyj analiz i issledovanie operacij, Tome 26 (2019) no. 1, pp. 33-54

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We propose a method for determining the number of sensors, their arrangement, and approximate lower bounds for the number of sensors for the multiple covering of an arbitrary closed bounded convex area in a plane. The problem of multiple covering is considered with restrictions on the minimal possible distances between the sensors and without such restrictions. To solve these problems, some 0–1 linear programming (LP) problems are constructed. We use a heuristic solution algorithm for 0–1 LP problems of higher dimensions. The results of numerical implementation are given and for some particular cases it is obtained that the number of sensors found can not be decreased. Tab. 1, illustr. 3, bibliogr. 42.
Keywords: wireless sensor network, multiple covering, $k$-fold covering, $k$-covering with circles of given radius, number of sensors for monitoring of given area, arrangement of sensors. 
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     title = {On the number and arrangement of sensors for~the~multiple covering of bounded plane~domains},
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Sh. I. Galiev; A. V. Khorkov. On the number and arrangement of sensors for~the~multiple covering of bounded plane~domains. Diskretnyj analiz i issledovanie operacij, Tome 26 (2019) no. 1, pp. 33-54. http://geodesic.mathdoc.fr/item/DA_2019_26_1_a2/