A fixed-parameter algorithm for guarding 1.5D terrains
نویسندگان
چکیده
منابع مشابه
A Fast 2-Approximation Algorithm for Guarding Orthogonal Terrains
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...
متن کاملA 4-Approximation Algorithm for Guarding 1.5-Dimensional Terrains
In the 1.5-dimensional terrain guarding problem we are given as input an x-monotone chain (the terrain) and asked for the minimum set of guards (points on the terrain) such that every point on the terrain is seen by at least one guard. It has recently been shown that the 1.5-dimensional terrain guarding problem is approximable to within a constant factor [3,7], though no attempt has been made t...
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Let P be a polygon with n vertices. We say that two points of P see each other if the line segment connecting them lies inside (the closure of) P . In this paper we present efficient approximation algorithms for finding the smallest set G of points of P so that each point of P is seen by at least one point of G, and the points of G are constrained to be belong to the set of vertices of an arbit...
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...
متن کاملGuarding Polyhedral Terrains
We prove that [n/2J vertex guards are always sufficient and sometimes necessary to guard the surface of an n-vertex polyhedral terrain. We also show that l(4n 4)/13J edge guards are sometimes necessary to guard the surface of an n-vertex polyhedral terrain. The upper bound on the number of edge guards is ln/3J (Everett and Rivera-Campo, 1994). Since both upper bounds are based on the four color...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2015
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2015.06.028