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Covering orthogonal polygons with sliding k-transmitters

Mahdavi, S. S ; Sharif University of Technology | 2020

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  1. Type of Document: Article
  2. DOI: 10.1016/j.tcs.2020.02.008
  3. Publisher: Elsevier B. V , 2020
  4. Abstract:
  5. In this paper, we consider a new variant of covering in an orthogonal art gallery problem where each guard is a sliding k-transmitter. Such a guard can travel back and forth along an orthogonal line segment, say s, inside the polygon. A point p is covered by this guard if there exists a point q∈s such that pq‾ is a line segment normal to s, and has at most k intersections with the boundary walls of the polygon. The objective is to minimize the sum of the lengths of the sliding k-transmitters to cover the entire polygon. In other words, the goal is to find the minimum total length of trajectories on which the guards can travel to cover the entire polygon. We prove that this problem is NP-hard when k=2, and present a 2-approximation algorithm for any fixed k≥2. The proposed algorithm also works well for an orthogonal polygon where the edges have thickness. © 2020 Elsevier B.V
  6. Keywords:
  7. Art gallery ; Covering ; K-transmitters ; Sliding camera ; Computational geometry ; Art gallery problem ; Boundary walls ; Covering ; Line segment ; Total length ; Transmitters
  8. Source: Theoretical Computer Science ; Volume 815 , May , 2020 , Pages 163-181
  9. URL: https://www.sciencedirect.com/science/article/abs/pii/S030439752030092X