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Tight Bounds for Beacon-Based Coverage in Simple Rectilinear Polygons

  • Sang Won Bae
  • Chan-Su Shin
  • Antoine Vigneron
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9644)

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.

Notes

Acknowledgments

We thank the anonymous referees for their helpful comments.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of Computer ScienceKyonggi UniversitySuwonKorea
  2. 2.Division of Computer and Electronic Systems EngineeringHankuk University of Foreign StudiesYonginKorea
  3. 3.Visual Computing CenterKing Abdullah University of Science and Technology (KAUST)ThuwalSaudi Arabia

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