TY - GEN

T1 - Improved PTASs for convex barrier coverage

AU - Carmi, Paz

AU - Katz, Matthew J.

AU - Saban, Rachel

AU - Stein, Yael

N1 - Publisher Copyright: © Springer International Publishing AG, part of Springer Nature 2018.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - Let R be a connected closed region in the plane and let S be a set of n points (representing mobile sensors) in the interior of R. We think of R’s boundary as a barrier which needs to be monitored. This gives rise to the barrier coverage problem, where one needs to move the sensors to the boundary of R, so that every point on the boundary is covered by one of the sensors. We focus on the variant of the problem where the goal is to place the sensors on R’s boundary, such that the distance (along R’s boundary) between any two adjacent sensors is equal to R’s perimeter divided by n and the sum of the distances traveled by the sensors is minimum. In this paper, we consider the cases where R is either a circle or a convex polygon. We present a PTAS for the circle case and explain how to overcome the main difficulties that arise when trying to adapt it to the convex polygon case. Our PTASs are significantly faster than the previous ones due to Bhattacharya et al. [4]. Moreover, our PTASs require efficient solutions to problems, which, as we observe, are equivalent to the circle-restricted and line-restricted Weber problems. Thus, we also devise efficient PTASs for these Weber problems.

AB - Let R be a connected closed region in the plane and let S be a set of n points (representing mobile sensors) in the interior of R. We think of R’s boundary as a barrier which needs to be monitored. This gives rise to the barrier coverage problem, where one needs to move the sensors to the boundary of R, so that every point on the boundary is covered by one of the sensors. We focus on the variant of the problem where the goal is to place the sensors on R’s boundary, such that the distance (along R’s boundary) between any two adjacent sensors is equal to R’s perimeter divided by n and the sum of the distances traveled by the sensors is minimum. In this paper, we consider the cases where R is either a circle or a convex polygon. We present a PTAS for the circle case and explain how to overcome the main difficulties that arise when trying to adapt it to the convex polygon case. Our PTASs are significantly faster than the previous ones due to Bhattacharya et al. [4]. Moreover, our PTASs require efficient solutions to problems, which, as we observe, are equivalent to the circle-restricted and line-restricted Weber problems. Thus, we also devise efficient PTASs for these Weber problems.

UR - http://www.scopus.com/inward/record.url?scp=85045977221&partnerID=8YFLogxK

U2 - https://doi.org/10.1007/978-3-319-89441-6_3

DO - https://doi.org/10.1007/978-3-319-89441-6_3

M3 - Conference contribution

SN - 9783319894409

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 26

EP - 40

BT - Approximation and Online Algorithms - 15th International Workshop, WAOA 2017, Revised Selected Papers

A2 - Solis-Oba, Roberto

A2 - Fleischer, Rudolf

PB - Springer Verlag

T2 - 15th Workshop on Approximation and Online Algorithms, WAOA 2017

Y2 - 7 September 2017 through 8 September 2017

ER -