منابع مشابه
Guarding Galleries and Terrains
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 Art Galleries by Guarding Witnesses
Let P be a simple polygon. We define a witness set W to be a set of points such that if any (prospective) guard set G guards W , then it is guaranteed that G guards P . We show that not all polygons admit a finite witness set. If a finite minimal witness set exists, then it cannot contain any witness in the interior of P ; all witnesses must lie on the boundary of P , and there can be at most o...
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...
متن کاملGuarding Rectangular Art Galleries by
Consider a rectangular art gallery divided into n rectangular rooms, such that any two rooms sharing a wall in common have a door connecting them. How many guards need to be stationed in the gallery so as to protect all of the rooms in our gallery? Notice that if a guard is stationed at a door, he will be able to guard two rooms. Our main aim in this paper is to show that Èn/2 ̆ guards are alway...
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ژورنال
عنوان ژورنال: Information Processing Letters
سال: 2006
ISSN: 0020-0190
DOI: 10.1016/j.ipl.2006.05.014