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An Optimal Algorithm for the 1-Searchability of Polygonal Rooms

  • Xuehou Tan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3742)

Abstract

The 1-searcher is a mobile guard who can see only along a ray emanating from his position and can continuously change the direction of the ray with bounded speed. A polygonal region P with a specified point d on its boundary is called a room, and denoted by (P, d). The room (P, d) is said to be 1-searchable if the searcher, starting at the point d, can eventually see a mobile intruder who moves arbitrarily fast inside P, without allowing the intruder to touch d. We present an optimal O(n) time algorithm to determine whether there is a point x on the boundary of P such that the room (P, x) is 1-searchable. This improves upon the previous O(n log n) time bound, which was established for determining whether or not a room (P, d) is 1-searchable, where d is a given point on the boundary of P.

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References

  1. 1.
    Bhattacharya, B.K., Ghosh, S.K.: Characterizing LR-visibility polygons and related problems. Comput. Geom. The. Appl. 18, 19–36 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Bhattacharya, B.K., Mukhopadhyay, A., Narasimhan, G.: Optimal algorithms for two-guard walkability of simple polygons. In: Dehne, F., Sack, J.-R., Tamassia, R. (eds.) WADS 2001. LNCS, vol. 2125, pp. 438–449. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  3. 3.
    Chazelle, B.: Triangulating a simple polygon in linear time. Discrte Comput. Geometry 6, 485–524 (1991)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Das, G., Heffernan, P.J., Narasimhan, G.: LR-visibility in polygons. Comput. Geom. Theory Appl. 7, 37–57 (1997)zbMATHMathSciNetGoogle Scholar
  5. 5.
    Guibas, L.J., Hershberger, J., Leven, D., Sharir, M., Tarjan, R.E.: Linear-time algorithms for visibility and shortest path problems inside triangulated simple polygons. Algorithmica 2, 209–233 (1987)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Guibas, L.J., Latombe, J.C., Lavalle, S.M., Lin, D., Motwani, R.: Visibility-based pursuit-evasion in a polygonal environment. Int. J. Comput. Geom. & Appl. 9, 471–493 (1999)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Icking, C., Klein, R.: The two guards problem. Int. J. Comput. Geom. & Appl. 2, 257–285 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    LaValle, S.M., Simov, B., Slutzki, G.: An algorithm for searching a polygonal region with a flashlight. Int. J. Comput. Geom. & Appl. 12, 87–113 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Lee, J.H., Shin, S.Y., Chwa, K.Y.: Visibility-based pursuit-evasion in a polygonal room with a door. In: Proc. 15th Annu. ACM Symp. Comput. Geom., pp. 281–290 (1999)Google Scholar
  10. 10.
    Lee, J.H., Park, S.M., Chwa, K.Y.: Searching a polygonal room with one door by a 1-searcher. Int. J. Comput. Geom. & Appl. 10, 201–220 (2000)zbMATHMathSciNetGoogle Scholar
  11. 11.
    Lee, J.H., Park, S.M., Chwa, K.Y.: Simple algorithms for searchng a polygon with flashlights. Inform. Process. Lett. 81, 265–270 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Suzuki, I., Yamashita, M.: Searching for mobile intruders in a polygonal region. SIAM J. Comp. 21, 863–888 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Suzuki, I., Tazoe, Y., Yamashita, M., Kameda, T.: Searching a polygonal region from the boundary. Int. J. Comput. Geom. & Appl. 11, 529–553 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Tan, X.: Efficient algorithms for searching a polygonal room with a door. In: Akiyama, J., Kano, M., Urabe, M. (eds.) JCDCG 2000. LNCS, vol. 2098, pp. 339–350. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  15. 15.
    Tan, X.: A characterization of polygonal regions searchable from the boundary. In: Akiyama, J., Baskoro, E.T., Kano, M. (eds.) IJCCGGT 2003. LNCS, vol. 3330, pp. 200–215. Springer, Heidelberg (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Xuehou Tan
    • 1
  1. 1.Tokai UniversityNumazuJapan

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