Survey of Terrain Guarding and Art Gallery Problems
نویسنده
چکیده
The terrain guarding problem and art gallery problem are two areas in computational geometry. Different versions of terrain guarding involve guarding a discrete set of points or a continuous set of points on a terrain. The art gallery problem has versions including guarding an entire polygon by a set of discrete points at the vertices or any point inside the polygon itself. This paper will give a survey as to what is known about each of these problems and what improvements could be worked on. This paper also provides a 4-approximation to the vertex terrain guarding problem.
منابع مشابه
Orthogonal Terrain Guarding is NP-complete
A terrain is an x-monotone polygonal curve, i.e., successive vertices have increasing x-coordinates. Terrain Guarding can be seen as a special case of the famous art gallery problem where one has to place at most k guards on a terrain made of n vertices in order to fully see it. In 2010, King and Krohn showed that Terrain Guarding is NP-complete [SODA ’10, SIAM J. Comput. ’11] thereby solving a...
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