Efficient band monitoring with sensors outer positioning

Astrakov, S. N.; Erzin, Adil

doi:10.1080/02331934.2013.840621

Cited by 6 publications

(9 citation statements)

References 7 publications

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“…for every [ 1,2] and R [R1, R2], where Z + is the set of positive integers, k( , R) is the number of sectors ( , R) with vertices at one point are involved to cover one tile, and S( , R) is the maximum area of an equilateral triangle inscribed in a sector ( k, R) (a sector is formed by k adjacent sectors with the angles , whose vertices are in the same point).…”

Section: Problem Formulationmentioning

confidence: 99%

“…In [5] proposed new covers of stripe with disks and found the densities of these covers. In [2] proposed several new regular covers of the stripe with disks when the placement of the centers of the disks within the band is prohibited. The last additional requirement arises naturally in many applications (monitoring the border strip, roads, rivers, pipelines, etc.…”

Section: Introductionmentioning

confidence: 99%

“…The cover of a plane region A is such set of figures C, that each point in A belongs to at least one figure in C. It is believed that the sensor's energy consumption is proportional to the covered area [2,3,5,6,18,24].…”

Section: Introductionmentioning

confidence: 99%

“…If[ 1,2] (0, /9], then it is necessary to compare the next four non-monotonic functions with several local minima.It is easy to prove that f1( ) > f2( ) and f4( ) > f3( ), so it is sufficient to compare functions f2( ) and f3( ). Denote the difference f2( ) -f3( ) divided by the 2 and multiplied by sign dozens of times, however, the number of sectors k( ) covering one tile can take only two valuesWe have f4( ) > f2( ).…”

mentioning

confidence: 99%

See 3 more Smart Citations

Covering the Plane with Equal Sectors

Erzin

Shabelnikova

Zalyubovskiy

2016

Proceedings of the 10th International Conference on Ubiquitous Information Management and Communication

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In the regular covers, a region in the plane is split into the equal regular polygons (tiles), and all the tiles are covered equally with some geometric figures. In this paper, a tile is an equilateral triangle. We proposed and analyzed the regular covers with equal sectors in which the number of sectors per unit area is minimal. The problem of minimizing the number of sectors per unit area is closely related to the problem of the least dense coverage, but does not coincide with it completely. We found the optimal number of sectors covering one tile in the case when every sector is involved in covering only one tile, and the vertices of the sectors which cover one tile are located in one point.The results can be used in different applications, for example, for design of the cost-effective sensor networks with equal directed sensors when the coverage area of the sensor is a sector.

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Section: Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Covering the Plane with Equal Sectors

Erzin

Shabelnikova

Zalyubovskiy

2016

Proceedings of the 10th International Conference on Ubiquitous Information Management and Communication

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“…Then the main goal in WSN is lifetime maximization [5,8,9,10,15,17,20,23]. If only sensing energy consumption is taken into account, then the problem can be reduced to the construction of the least density covers [3,5,7,16,21,23].…”

Section: Introductionmentioning

confidence: 99%

Sensor Networks and Optimal Regular Covering of the Plane With Equal Sectors

Erzin¹,

Shabelnikova²

2015

Proceedings of the 2015 International Conference on Electrical, Automation and Mechanical Engineering

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We suppose that in the sensor network, the sensing areas of the sensors are equal sectors, and consider the problem of regular covering of the plane with minimal number of identical sensors per unit area. In the regular cover, the plane is split into the equal regular polygons -"tiles" (equilateral triangles, squares or regular hexagons), and all the tiles are covered equally. We solved the problem for the special case when every sensor covers one tile, and all the sensors covering one tile are placed in one point.

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Comparative analysis of regular covers with one or two types of sectors

Erzin¹,

Osotova²

2016

AIP Conference Proceedings

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Efficient band monitoring with sensors outer positioning

Cited by 6 publications

References 7 publications

Covering the Plane with Equal Sectors

Covering the Plane with Equal Sectors

Sensor Networks and Optimal Regular Covering of the Plane With Equal Sectors

Comparative analysis of regular covers with one or two types of sectors

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