Optimization Algorithms for Sweeping a Polygonal Region with Mobile Guards
Abstract

 Given an nsided polygon, we present an O(n^{2} log n)time algorithm for computing a shortest walk in which the total length of the paths that two guards traverse is minimized.

 Given an nsided polygon, we present an O(n^{2})time algorithm for computing a minimum diameter walk in which the maximum distance between two guards is minimized.
Finally we allow more than two guards. Here the guards should form a simple chain within the polygon such that any consecutive two guards along the chain are mutually visible and the first and last guard have to move along the boundary but others do not.  We present an O(n^{2})time algorithm for computing the minimum number of guards to sweep an nsided polygon and an O(n^{3})time algorithm for computing such a schedule.
Preview
Unable to display preview. Download preview PDF.
References
 1.B. Bhattacharya, A. Mukhopadhyay, and G. Narasimhan. Twoguard walkability of simple polygons. In Proc. of 7th WADS, 2001.Google Scholar
 2.D. Crass, I. Suzuki, and M. Yamashita. Searching for a mobile intruder in a corridorthe open edge variant of the polygon search problem. Int. J. of Comp. Geom. and Appl., 5(4):397–412, 1995.MathSciNetCrossRefzbMATHGoogle Scholar
 3.A. Efrat, L. Guibas, S. HarPeled, D. Lin, J. Mitchell, and T. Murali. Sweeping simple polygons with a chain of guards. In Proc. of 16th Symp. on Discrete Algorithm, pages 927–936, 2000.Google Scholar
 4.L. Guibas, J. Hershberger, D. Leven, M. Sharir, and R. Tarjan. Lineartime algorithms for visibility and shortest path problems inside triangulated simple polygon. Algorithmica, 2:209–233, 1987.MathSciNetCrossRefzbMATHGoogle Scholar
 5.L. J. Guibas, J. C. Latombe, S. M. Lavalle, D. Lin, and R. Motwani. A visibilitybased pursuitevasion problem. Int. J. of Comp. Geom. and Appl., 9(4):471–493, 1999.MathSciNetCrossRefGoogle Scholar
 6.P. J. Heffernan. An optimal algorithm for the twoguard problem. Int. J. of Comp. Geom. and Appl., 6(1):15–44, 1996.MathSciNetCrossRefzbMATHGoogle Scholar
 7.C. Icking and R. Klein. The two guards problem. Int. J. of Comp. Geom. and Appl., 2(3):257–285, 1992.MathSciNetCrossRefzbMATHGoogle Scholar
 8.S. M. LaValle, B. H. Simov, and G. Slutzki. An algorithm for searching a polygonal region with a flashlight. In Proc. of 16th Symp. on Computational Geometry, 2000.Google Scholar
 9.JaeHa Lee, SangMin Park, and KyungYong Chwa. Searching a polygonal room with one door by a 1searcher. Int. J. of Comp. Geom. and Appl., 10(2), 2000.Google Scholar
 10.JaeHa Lee, Sung Yong Shin, and KyungYong Chwa. Visibilitybased pursuitevasion in a polygonal room with a door. In Proc. 15th ACM Sympos. on Computational Geometry, pages 281–290, 1999.Google Scholar
 11.G. Narashimhan. On hamiltonian triangulations in simple polygons. Int. J. of Comp. Geom. and Appl., 9(3):261–275, 1999.MathSciNetCrossRefGoogle Scholar
 12.SangMin Park, JaeHa Lee, and KyungYong Chwa. Visibilitybased pursuitevasion in a polygonal region by a single searcher. In Proc. of ICALP, pages 456–468, 2001.Google Scholar
 13.S. Suri. On some link distance problems in a simple polygon. IEEE Trans. Robot. Autom., 6:108–113, 1990.CrossRefGoogle Scholar
 14.I. Suzuki and M. Yamashita. Searching for a mobile intruder in a polygonal region.SIAM J. Comp., 21(5):863–888, 1992.MathSciNetCrossRefzbMATHGoogle Scholar
 15.L. H. Tseng, P. Heffernan, and D. T. Lee. Twoguard walkability of simple polygons. Int. J. of Comp. Geom. and Appl., 8:85–116, 1998.MathSciNetCrossRefzbMATHGoogle Scholar