Abstract
We establish tight bounds for beacon-based coverage problems. In particular, we show that \(\lfloor \frac{n}{6} \rfloor \) beacons are always sufficient and sometimes necessary to cover a simple rectilinear polygon P with n vertices. When P is monotone and rectilinear, we prove that this bound becomes \(\lfloor \frac{n+4}{8} \rfloor \). We also present an optimal linear-time algorithm for computing the beacon kernel of P.
Work by S.W.Bae was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (2013R1A1A1A05006927) and by the Ministry of Education (2015R1D1A1A01057220). Work by C.-S. Shin was supported by Research Grant of Hankuk University of Foreign Studies. Work by A. Vigneron was supported by KAUST base funding.
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Notes
- 1.
A chord c of a polygon is a line segment between two points on the boundary such that all points on c except the two endpoints lie in the interior of the polygon.
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We thank the anonymous referees for their helpful comments.
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Bae, S.W., Shin, CS., Vigneron, A. (2016). Tight Bounds for Beacon-Based Coverage in Simple Rectilinear Polygons. In: Kranakis, E., Navarro, G., Chávez, E. (eds) LATIN 2016: Theoretical Informatics. LATIN 2016. Lecture Notes in Computer Science(), vol 9644. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-49529-2_9
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