Guarding Terrains via Local Search
نویسندگان
چکیده
We obtain a polynomial time approximation scheme for the 1.5D terrain guarding problem, improving upon several recent constant factor approximations. Our algorithm is a local search algorithm inspired by the recent results of Chan and Har-Peled [3] and Mustafa and Ray [18]. Our key contribution is to show the existence of a planar graph that appropriately relates the local and global optimum.
منابع مشابه
VC-Dimension of Visibility on Terrains
A guarding problem can naturally be modeled as a set system (U ,S) in which the universe U of elements is the set of points we need to guard and our collection S of sets contains, for each potential guard g, the set of points from U seen by g. We prove bounds on the maximum VC-dimension of set systems associated with guarding both 1.5D terrains (monotone chains) and 2.5D terrains (polygonal ter...
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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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متن کاملGuarding Orthogonal Terrains
A 1.5-dimensional terrain T with n vertices is an xmonotone polygonal chain in the plane. A point guard p on T guards a point q of T if the line segment connecting p to q lies on or above T ; p is a vertex guard if it is a vertex of T . In the Optimal Terrain Guarding (OTG) problem on T , the objective is to guard the vertices of T by the minimum number of vertex guards. King and Krohn [9] show...
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ورودعنوان ژورنال:
- JoCG
دوره 5 شماره
صفحات -
تاریخ انتشار 2014