Abstract
Given a simple polygon P with two vertices u and v, the two-guard problem asks if two guards can move on the boundary chains of P from u to v, one clockwise and one counterclockwise, such that they are mutually visible. By a close study of the structure of the restrictions placed on the motion of two guards, we present a simpler solution to the two-guard problem. The main goal of this paper is to extend the solution for the two-guard problem to that for the three-guard problem, in which the first and third guards move on the boundary chains of P from u to v and the second guard is always kept to be visible from them inside P. By introducing the concept of link-2-ray shots, we show a one-to-one correspondence between the structure of the restrictions placed on the motion of two guards and the one placed on the motion of three guards. We can decide if there exists a solution for the three-guard problem in O(n log n) time, and if so generate a walk in O(n log n + m) time, where n denotes the number of vertices of P and m (≤ n 2) the size of the optimal walk.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
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)
Crass, D., Suzuki, I., Yamashita, M.: Search for a mobile intruder in a corridor. In: IJCGA, vol. 5, pp. 397–412 (1995)
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 SODA, pp. 927–936 (2000)
Heffernan, P.J.: An optimal algorithm for the two-guard problem. In: IJCGA, vol. 6, pp. 15–44 (1996)
Icking, C., Klein, R.: The two guards problem. In: IJCGA, vol. 2, pp. 257–285 (1992)
Suzuki, I., Yamashita, M.: Searching for mobile intruders in a polygonal region. SIAM J. Comp. 21, 863–888 (1992)
Tseng, L.H., Heffernan, P.J., Lee, D.T.: Two-guard walkability of simple polygons. In: IJCGA, vol. 8, pp. 85–116 (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Tan, X. (2004). The Two-Guard Problem Revisited and Its Generalization. In: Fleischer, R., Trippen, G. (eds) Algorithms and Computation. ISAAC 2004. Lecture Notes in Computer Science, vol 3341. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30551-4_72
Download citation
DOI: https://doi.org/10.1007/978-3-540-30551-4_72
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24131-7
Online ISBN: 978-3-540-30551-4
eBook Packages: Computer ScienceComputer Science (R0)