Abstract
The polygon search problem is the problem of searching for a mobile intruder in a simple polygon by the mobile searcher who holds flashlights and whose visibility is limited to the rays emanating from his flashlights. The goal is to decide whether there exists a search schedule for the searcher to detect the intruder, no matter how fast he moves, and if so, generate such a schedule. A searcher is called the k-searcher if he can see along k rays emanating from his position, and the∞-searcher if he has a 360° field of vision. We present necessary and sufficient conditions for a polygon to be searchable by a k-searcher (for k = 1 or 2), and give O(n 2) time algorithms for testing the k-searchability of simple polygons and generating a search schedule if it exists. We also show that any polygon that is searchable by an ∞-searcher is searchable by a 2-searcher. Our results solve a long-standing open problem in computational geometry and robotics, and confirm a conjecture due to Suzuki and Yamashita.
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References
W.P. Chin and S. Ntafos, Shortest watchman routes in simple polygons, Disc. Comp. Geom. 6, (1991) 9–31.
D. Crass, I. Suzuki and M. Yamashita, Searching for a mobile intruder in a corridor, Int. J. Comput. Geom. & Appl. 5 (1995) 397–412.
L.J. Guibas, J. Hershberger, D. Leven, M. Sharir and R.E. Tarjan, Linear-time algorithms for visibility and shortest path problems inside triangulated simple polygons, Algorithmica, 2 (1987) 209–233.
L.J. Guibas, J.C. Latombe, S.M. Lavalle, D. Lin and R. Motwani, Finding an unpredictable target in a workspace with obstacle, in Proc. IEEE int. Conf. Robotics and Automation, 1997.
L.J. Guibas, J.C. Latombe, S.M. Lavalle, D. Lin and R. Motwani, Visibility-based pursuit-evasion in a polygonal environment, Int. J. Comp. Geom. & Appl. 9, (1999) 471–493.
P.J. Heffernan, An optimal algorithm for the two-guard problem, Int. J. Comput. Geom. & Appl. 6 (1996) 15–44.
C. Icking and R. Klein, The two guards problem, Int. J. Comput. Geom. & Appl. 2 (1992) 257–285.
S.M. LaValle, B. Simov and G. Slutzki, An algorithm for searching a polygonal region with a flashligh, Proc. 16th Annu. ACM Symp. Comput. Geom.
J.H. Lee, S.Y. Shin and K.Y. Chwa, Visibility-based pursuit-evasion in a polygonal room with a door, Proc. 15th Annu. ACM Symp. Comput. Geom. (1999) 281–290.
T. Shermer, Recent results in art galleries Proceedings of IEEE 80 (1992) 1384–1399.
I. Suzuki and M. Yamashita, Searching for mobile intruders in a polygonal region, SIAM J. Comp. 21 (1992) 863–888.
I. Suzuki, M. Yamashita, H. Umemoto and T. Kameda, Bushiness and a tight worst-case upper bound on the search number of a simple polygon, Inform. Process. Lett. 66 (1998) 49–52.
X. Tan, T. Hirata and Y. Inagaki, An incremental algorithm for constructing shortest watchman routes, Int. J. Comp. Geom. & Appl. 3, (1993) 351–365.
X. Tan, T. Hirata and Y. Inagaki, “Corrigendum to “An incremental algorithm for constructing shortest watchman routes”, Int. J. Comp. Geom. & Appl. 3, (1999) 319–323.
X. Tan, An efficient solution to the corridor search problem, Lect. Notes Comput. Sci. 1763 (Proc. JCDCG’98) (2000) 317–332.
M. Yamashita, H. Umemoto, I. Suzuki and T. Kameda, “Searching for mobile intruders in a polygonal region by a group of mobile searchers”. In Pro. 13th Annu. ACM Symp. Comput. Geom. (1997) 448–450.
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Tan, X. (2000). Searching a Simple Polygon by a k-Searcher. In: Goos, G., Hartmanis, J., van Leeuwen, J., Lee, D.T., Teng, SH. (eds) Algorithms and Computation. ISAAC 2000. Lecture Notes in Computer Science, vol 1969. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-40996-3_43
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DOI: https://doi.org/10.1007/3-540-40996-3_43
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