Improved PTASs for convex barrier coverage

Paz Carmi, Matthew J. Katz, Rachel Saban, Yael Stein

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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.

Original languageAmerican English
Title of host publicationApproximation and Online Algorithms - 15th International Workshop, WAOA 2017, Revised Selected Papers
EditorsRoberto Solis-Oba, Rudolf Fleischer
PublisherSpringer Verlag
Number of pages15
ISBN (Print)9783319894409
StatePublished - 1 Jan 2018
Event15th Workshop on Approximation and Online Algorithms, WAOA 2017 - Vienna, Austria
Duration: 7 Sep 20178 Sep 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10787 LNCS


Conference15th Workshop on Approximation and Online Algorithms, WAOA 2017

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science


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