A Fast 2-Approximation Algorithm for Guarding Orthogonal Terrains
نویسندگان
چکیده
Terrain Guarding Problem(TGP), which is known to be NP-complete, asks to find a smallest set of guard locations on a terrain T such that every point on T is visible by a guard. Here, we study this problem on 1.5D orthogonal terrains where the edges are bound to be horizontal or vertical. We propose a 2-approximation algorithm that runs in O(n logm) time, where n and m are the sizes of input and output, respectively. This is an improvement over the previous best algorithm, which is a 2-approximation with O(n) running time.
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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