Barrier Covering in 2D Using Mobile Sensors with Circular Coverage Areas

摘要

In the problem of barrier monitoring using mobile sensors with circular coverage areas, it is required to move the sensors onto some line (barrier) so that each barrier point belongs to the coverage area of at least one sensor. One of the criteria for the effectiveness of coverage is the minimum of the total length of the paths traveled by sensors. If we give up the requirement to move the sensors onto the barrier, then the problem (which is NP-hard) will not be easier. But at the same time, the value of the objective function can be reduced significantly. In this paper, we propose a new pseudo-polynomial algorithm which in the case of equal disks builds an optimal solution in the L metric and a /2-approximate solution in the Euclidean metric. This algorithm is an efficient implementation of the dynamic programming method in which at the stage of preliminary calculations for each sensor it is possible to find a finite number of analytical functions equal to the minimal length of the path traveled by the sensor depending on the positions of the circle and the barrier. The conducted numerical experiment showed that if we remove the requirement to move the sensors onto the barrier, then the value of the objective function may decrease several times.