TY - JOUR

T1 - Coverings of sets with restrictions on the arrangement of circles

AU - Astrakov, Sergey N.

PY - 2017

Y1 - 2017

N2 - Coverings of sets and domains by a system of circles whose centers have restrictions on their arrangement are considered. From the sensorrelated perspective, this corresponds to the sensor coverage problem, where the network sensors control objects or a region of space, but are located outside the control area. Formalizing the problem, we arrive at the problem of discrete geometry to determine the optimal number of circles, their sizes and locations, which provide the minimum coverage density of a given set. New results for the optimal outer covering of a circle, a square and a regular triangle are presented. The study of these models opens a possibility of building a sensor network with a minimal energy consumption.

AB - Coverings of sets and domains by a system of circles whose centers have restrictions on their arrangement are considered. From the sensorrelated perspective, this corresponds to the sensor coverage problem, where the network sensors control objects or a region of space, but are located outside the control area. Formalizing the problem, we arrive at the problem of discrete geometry to determine the optimal number of circles, their sizes and locations, which provide the minimum coverage density of a given set. New results for the optimal outer covering of a circle, a square and a regular triangle are presented. The study of these models opens a possibility of building a sensor network with a minimal energy consumption.

UR - http://www.scopus.com/inward/record.url?scp=85036647810&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85036647810

VL - 1987

SP - 67

EP - 72

JO - CEUR Workshop Proceedings

JF - CEUR Workshop Proceedings

SN - 1613-0073

ER -