Journal of the Korea Society of Computer and Information (한국컴퓨터정보학회논문지)

Korean Society of Computer Information (한국컴퓨터정보학회)
권호 표지
DOI QR코드

DOI QR Code

A Simple Polygon Search Algorithm

  • Lee, Sang-Un (Dept. of Multimedia Engineering, Gangneung-Wonju National University)
  • Received : 2016.03.19
  • Accepted : 2016.04.26
  • Published : 2016.05.31
Download PDF
⟨ Previous Next ⟩

Abstract

This paper considers simple polygon search problem. How many searchers find a mobile intruder that is arbitrarily faster than the searcher within polygon art gallery? This paper uses the visibility graph that is connected with edges for mutually visible vertices. Given visibility graph, we select vertex u that is conjunction ${\Delta}(G)$ in $N_G(v)$ for $d_G(v){\leq}4$. We decide 1-searchable if $1{\leq}{\mid}u{\mid}{\leq}2$ and 2-searchable if ${\mid}u{\mid}{\geq}3$. We also present searcher's shortest path. This algorithm is verified by varies 1 or 2-searchable polygons.

Keywords

References

  1. I. Suzuki, and M. Yamasita, "Searching for a Mobile Intruder in a Polygon Region," SIAM Journal on Computing, Vol. 21, No. 5, pp. 863-888, 1992. https://doi.org/10.1137/0221051
  2. M. Yamashita, H. Umemoto, I. Suzuki, and T. Kameda, "Searching for Mobile Intruders in a Polygonal Region by a Group of Mobile Searchers," SIAM Journal on Computing, Vol. 21, pp. 863-888, 1996.
  3. X. Tan, "Searching a Simple Polygon by a k-Searcher," Lecture Notes in Computer Science (LNCS), Vol. 1969, pp. 503-514, 2000.
  4. S. M. LaValle, B. Simov, and G. Slutzki, "An Algorithm for Searching a Polygonal Region with a Flashlight," International Journal of Computational Geometry and Applications (IJCGA), pp. 260-269, 2000.
  5. J. H. Lee, S. M. Park, and K. Y. Chwa, "Simple Algorithms for Searching a Polygon with Flashlights," Information Processing Letters, Vol. 81, pp. 265-270, 2002. https://doi.org/10.1016/S0020-0190(01)00235-6
  6. J. Z. Zhang and T. Kameda, "Where to Build a Door," Technical Report, CMPT2006-14, Department of Math and Computer Science, University of Lethbridge, Canada, 2006.
  7. T. Kameda, I. Suzuki, and J. Z. Zhang, "Minimization of Distance Traveled in Surveillance of a Polygonal Region from the Boundary," Japan Conference on Computational Geometry and Graphs (JCCGG), 2009.
  8. S. Bahun and A. Lubiw, 'Optimal Schedules for 2-Guard Room Search," CCCG, 2007.
  9. B. Bhattacharya, J. Z. Zhang, Q. Shi, and T. Kameda, "An Optimal Solution to Room Search Problem," Technical Report, CMPT2006-16, School of Computing Science, Simon Fraser University, Canada, 2006.
  10. S. U. Lee, "Minimum number of Vertex Guards Algorithm for Art Gallery Problem," Journal of KSCI, Vol. 16, No. 6, pp. 179-186, Jun. 2011.
  11. S. U. Lee and M. B. Choi, "The Minimum number of Mobile Guards Algorithm for Art Gallery Problem," Journal of IIBC, Vol. 12, No. 3, pp. 63-69, Jun. 2012.
  12. Wikipedia, "Art Gallery Problem," http://en.wikipedia.org/wiki/Art_gallery_problem, 2016.
  13. N. Do, "Art Gallery Theorems," www.austms.org.au/Publ/Gazette/2004/Nov04/mathellaneous.pdf, 2004.
  14. J. Urrutia, "Art Gallery and Illumination Problems," Handbook of Computational Geometry, Department of Computer Science, University of Ottawa, Canada, 1996.
  15. I. Peterson, "Problem at the Art Gallery," http://www.maa.org/mathland/mathland_11_4.html, 1996.
  16. S. K. Ghosh, "Art Gallery Theorems and Approximation Algorithms," School of Technology & Computer Science, Teta Institute of Fundamental Research, Mumbai, India, 2010.
  17. T. C. Shermer, "Recent Results in Art Galleries," Proceedings of the IEEE, Vol. 80, No. 9, 1992.
  18. V. Isler, S. Kannan, and S. Khanna, "Locating and Capturing an Evader in a Polygonal Environment," In Proceedings of the Sixth International Workshop on Algorithmic Foundations of Robotics (WAFR'04), pp. 351-367, 2004.