Document Open Access Logo

Illuminating the x-Axis by α-Floodlights

Authors Bengt J. Nilsson , David Orden , Leonidas Palios , Carlos Seara , Paweł Żyliński

PDF

File

Thumbnail PDF
PDF
LIPIcs.ISAAC.2021.11.pdf
  • Filesize: 1.11 MB
  • 12 pages

Document Identifiers

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • Computational Geometry
  • Visibility
  • Art Gallery Problems
  • Floodlights

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

Abstract

Given a set S of regions with piece-wise linear boundary and a positive angle α < 90°, we consider the problem of computing the locations and orientations of the minimum number of α-floodlights positioned at points in S which suffice to illuminate the entire x-axis. We show that the problem can be solved in O(n log n) time and O(n) space, where n is the number of vertices of the set S.

Cite As Get BibTex

Bengt J. Nilsson, David Orden, Leonidas Palios, Carlos Seara, and Paweł Żyliński. Illuminating the x-Axis by α-Floodlights. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 11:1-11:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.ISAAC.2021.11

Author Details

Bengt J. Nilsson
  • Department of Computer Science and Media Technology, Malmö University, Sweden
David Orden
  • Physics and Mathematics Department, Universidad de Alcalá, Spain
Leonidas Palios
  • Department of Computer Science and Engineering, University of Ioannina, Greece
Carlos Seara
  • Departament of Mathematics, Universitat Politècnica de Catalunya, Barcelona, Spain
Paweł Żyliński
  • Institute of Informatics, University of Gdańsk, Poland

Funding

  • Nilsson, Bengt J.: Grant 2018-04001 from the Swedish Research Council.
  • Orden, David: H2020-MSCA-RISE project 734922-CONNECT and project PID2019-104129GB-I00 funded by MCIN/ AEI /10.13039/501100011033.
  • Seara, Carlos: H2020-MSCA-RISE project 734922-CONNECT and projects PID2019-104129GB-I00/ AEI/ 10.13039/501100011033 and Gen. Cat. DGR 2017SGR1640.

References

  1. Ahmed Abdelkader, Ahmed Saeed, Khaled A. Harras, and Amr Mohamed. The inapproximability of illuminating polygons by α-floodlights. In Proceedings of the 27th Canadian Conference on Computational Geometry, CCCG 2015, Kingston, Ontario, Canada, August 10-12, 2015. Queen’s University, Ontario, Canada, 2015. URL: http://research.cs.queensu.ca/cccg2015/CCCG15-papers/25.pdf.
  2. Sergey Bereg, José Miguel Díaz-Báñez, Marta Fort, Mario Alberto López, Pablo Pérez-Lantero, and Jorge Urrutia. Continuous surveillance of points by rotating floodlights. Int. J. Comput. Geom. Appl., 24(3):183-196, 2014. URL: https://doi.org/10.1142/S0218195914600024.
  3. Prosenjit Bose, Leonidas J. Guibas, Anna Lubiw, Mark H. Overmars, Diane L. Souvaine, and Jorge Urrutia. The floodlight problem. Int. J. Comput. Geom. Appl., 7(1/2):153-163, 1997. URL: https://doi.org/10.1142/S0218195997000090.
  4. Jurek Czyzowicz, Stefan Dobrev, Benson L. Joeris, Evangelos Kranakis, Danny Krizanc, Ján Manuch, Oscar Morales-Ponce, Jaroslav Opatrny, Ladislav Stacho, and Jorge Urrutia. Monitoring the plane with rotating radars. Graphs Comb., 31(2):393-405, 2015. URL: https://doi.org/10.1007/s00373-015-1543-4.
  5. Jurek Czyzowicz, Eduardo Rivera-Campo, and Jorge Urrutia. Optimal floodlight illumination of stages. In Proceedings of the 5th Canadian Conference on Computational Geometry, Waterloo, Ontario, Canada, August 1993, pages 393-398. University of Waterloo, 1993. Google Scholar
  6. Mark de Berg, Otfried Cheong, Marc J. van Kreveld, and Mark H. Overmars. Computational Geometry: Algorithms and Applications, 3rd Edition. Springer, 2008. URL: https://www.worldcat.org/oclc/227584184.
  7. Jana Dietel, Hans-Dietrich Hecker, and Andreas Spillner. A note on optimal floodlight illumination of stages. Inf. Process. Lett., 105(4):121-123, 2008. URL: https://doi.org/10.1016/j.ipl.2007.08.009.
  8. Vladimir Estivill-Castro, Joseph O'Rourke, Jorge Urrutia, and Dianna Xu. Illumination of polygons with vertex lights. Inf. Process. Lett., 56(1):9-13, 1995. URL: https://doi.org/10.1016/0020-0190(95)00129-Z.
  9. Vladimir Estivill-Castro and Jorge Urrutia. Two-floodlight illumination of convex polygons. In Selim G. Akl, Frank K. H. A. Dehne, Jörg-Rüdiger Sack, and Nicola Santoro, editors, Algorithms and Data Structures, 4th International Workshop, WADS '95, Kingston, Ontario, Canada, August 16-18, 1995, Proceedings, volume 955 of Lecture Notes in Computer Science, pages 62-73. Springer, 1995. URL: https://doi.org/10.1007/3-540-60220-8_51.
  10. Christodoulos Fragoudakis, Euripides Markou, and Stathis Zachos. Maximizing the guarded boundary of an art gallery is apx-complete. Comput. Geom., 38(3):170-180, 2007. URL: https://doi.org/10.1016/j.comgeo.2006.12.001.
  11. Hiro Ito, Hideyuki Uehara, and Mitsuo Yokoyama. NP-completeness of stage illumination problems. In Jin Akiyama, Mikio Kano, and Masatsugu Urabe, editors, Discrete and Computational Geometry, Japanese Conference, JCDCG'98, Tokyo, Japan, December 9-12, 1998, Revised Papers, volume 1763 of Lecture Notes in Computer Science, pages 158-165. Springer, 1998. URL: https://doi.org/10.1007/978-3-540-46515-7_12.
  12. Aldo Laurentini. Guarding the walls of an art gallery. Vis. Comput., 15(6):265-278, 1999. URL: https://doi.org/10.1007/s003710050177.
  13. Joseph O'Rourke. Art Gallery Theorems and Algorithms. Oxford University Press, Inc., USA, 1987. Google Scholar
  14. Joseph O'Rourke. Visibility. In Jacob E. Goodman and Joseph O'Rourke, editors, Handbook of Discrete and Computational Geometry, Second Edition, pages 643-663. Chapman and Hall/CRC, 2004. URL: https://doi.org/10.1201/9781420035315.ch28.
  15. T.C. Shermer. Recent results in art galleries (geometry). Proceedings of the IEEE, 80(9):1384-1399, 1992. URL: https://doi.org/10.1109/5.163407.
  16. Sven Skyum. A simple algorithm for computing the smallest enclosing circle. Inf. Process. Lett., 37(3):121-125, 1991. URL: https://doi.org/10.1016/0020-0190(91)90030-L.
  17. William L. Steiger and Ileana Streinu. Illumination by floodlights. Comput. Geom., 10(1):57-70, 1998. URL: https://doi.org/10.1016/S0925-7721(97)00027-8.
  18. Kazuo Sugihara, Ichiro Suzuki, and Masafumi Yamashita. The searchlight scheduling problem. SIAM J. Comput., 19(6):1024-1040, 1990. URL: https://doi.org/10.1137/0219070.
  19. Dan Tao and Tin-Yu Wu. A survey on barrier coverage problem in directional sensor networks. IEEE Sensors Journal, 15(2):876-885, 2015. URL: https://doi.org/10.1109/JSEN.2014.2310180.
  20. Jorge Urrutia. Art gallery and illumination problems. In Jörg-Rüdiger Sack and Jorge Urrutia, editors, Handbook of Computational Geometry, pages 973-1027. North Holland / Elsevier, 2000. URL: https://doi.org/10.1016/b978-044482537-7/50023-1.
  21. Izu Vaisman. Analytical Geometry. World Scientific, 1997. URL: https://doi.org/10.1142/3494.
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact