Abstract
A polygon P admits a sweep if two mobile guards can detect an unpredictable, moving target inside P, no matter how fast the target moves. For safety, two guards are required to always be mutually visible, and thus, they should move on the polygon boundary. Our objective in this paper is to find an optimum sweep such that the sum of the distances travelled by the two guards in the sweep is minimized. We present an O(n 2) time and O(n) space algorithm, where n is the number of vertices of the given polygon. This new result is obtained by converting the problem of sweeping simple polygons with two guards into that of finding a shortest path between two nodes in a graph of size O(n).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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)
Chazelle, B., Guibas, L.: Visibility and intersection problem in plane geometry. Discrete Comput. Geom. 4, 551–581 (1989)
Efrat, A., Guibas, L.J., Har-Peled, S., Lin, D.C., Mitchell, J.S.B., Murali, T.M.: Sweeping simple polygons with a chain of guards. In: Proc., ACM-SIAM Sympos. Discrete Algorithms, pp. 927–936 (2000)
Guibas, L.J., Latombe, J.C., Lavalle, S.M., Lin, D., Motwani, R.: Visibility-based pursuit-evasion in a polygonal environment. IJCGA 9, 471–493 (1999)
Heffernan, P.J.: An optimal algorithm for the two-guard problem. IJCGA 6, 15–44 (1996)
Icking, C., Klein, R.: The two guards problem. IJCGA 2, 257–285 (1992)
LaValle, S.M., Simov, B., Slutzki, G.: An algorithm for searching a polygonal region with a flashlight. IJCGA 12, 87–113 (2002)
Lee, J.H., Park, S.M., Chwa, K.Y.: Searching a polygonal room with one door by a 1-searcher. IJCGA 10, 201–220 (2000)
Park, S.M., Lee, J.H., Chwa, K.Y.: Visibility-based pursuit-evasion in a polygonal region by a searcher. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds.) ICALP 2001. LNCS, vol. 2076, pp. 456–468. Springer, Heidelberg (2001)
Suzuki, I., Yamashita, M.: Searching for mobile intruders in a polygonal region. SIAM J. Comp. 21, 863–888 (1992)
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)
Tan, X.: The two-guard problem revisited and its generalization. In: Fleischer, R., Trippen, G. (eds.) ISAAC 2004. LNCS, vol. 3341, pp. 847–858. Springer, Heidelberg (2004)
Tan, X.: Sweeping simple polygons with the minimum number of chain guards. Inform. Process. Lett. 102, 66–71 (2007)
Tan, X., Jiang, B.: Searching a polygonal region by two guards. J. Comput. Sci. Tech. 23(5), 728–739 (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Tan, X., Jiang, B. (2010). Optimum Sweeps of Simple Polygons with Two Guards. In: Lee, DT., Chen, D.Z., Ying, S. (eds) Frontiers in Algorithmics. FAW 2010. Lecture Notes in Computer Science, vol 6213. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14553-7_29
Download citation
DOI: https://doi.org/10.1007/978-3-642-14553-7_29
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14552-0
Online ISBN: 978-3-642-14553-7
eBook Packages: Computer ScienceComputer Science (R0)