Finding the shortest watchman route in a simple polygon
We present the first polynomial-time algorithm that finds the shortest route in a simple polygon such that all points of the polygon is visible from some point on the route. This route is sometimes called the shortest watchman route, and it does not allow any restrictions on the route or on the simple polygon. Our algorithm runs in O(n3) time.
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- A. Aggarwal. The Art Gallery Theorem: Its Variations, Applications and Algorithmic Aspects. PhD thesis, Johns Hopkins University, 1984.Google Scholar
- B. Chazelle. Triangulating a Simple Polygon in Linear Time. In Proc. 31st Symposium on Foundations of Computer Science, pages 220–230, 1990.Google Scholar
- W. Chin, S. Ntafos. Shortest Watchman Routes in Simple Polygons. Discrete and Computational Geometry, 6(1):9–31, 1991.Google Scholar
- J.S.B. Mitchell, E.L. Wynters. Watchman Routes for Multiple Guards. In Proc. 3rd Canadian Conference on Computational Geometry, pages 126–129, 1991.Google Scholar
- B.J. Nilsson, S. Schuierer. Shortest m-Watchmen Routes for Histograms: The MinMax Case. Technical Report “Bericht 43”, Institut für Informatik, Universität Freiburg, Germany, January 1992. An extended abstract was presented at the 4th International Conference on Computing and Information, pages 31–34, 1992.Google Scholar
- B.J. Nilsson, D. Wood. Watchmen Routes in Spiral Polygons. Technical Report LU-CS-TR:90-55, Dept. of Computer Science, Lund University, 1990. An extended abstract of a preliminary version was presented at the 2nd Canadian Conference on Computational Geometry, pages 269–272, 1990.Google Scholar
- X.-H. Tan, T. Hirata, Y. Inagaki. An Incremental Algorithm for Constructing Shortest Watchman Routes. In Proc. ISA '91 Algorithms, pages 163–175. Springer Verlag, Lecture Notes in Computer Science 557, 1991.Google Scholar