Approximation algorithms for art gallery problems in polygons
نویسندگان
چکیده
منابع مشابه
Fast Approximation Algorithms for Art Gallery Problems in Simple Polygons
We present approximation algorithms with O(n) processing time for the minimum vertex and edge guard problems in simple polygons. It is improved from previous O(n) time algorithms of Ghosh. For simple polygon, there are O(n) visibility regions, thus any approximation algorithm for the set covering problem with approximation ratio of log(n) can be used for the approximation of n vertex and edge g...
متن کاملApproximation algorithms for art gallery problems in polygons
In this paper, we present approximation algorithms for minimum vertex and edge guard problems for polygonswith or without holes with a total of n vertices. For simple polygons, approximation algorithms for both problems run in O(n4) time and yield solutions that can be at most O(log n) times the optimal solution. For polygons with holes, approximation algorithms for both problems give the same ...
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The art gallery problem is to determine the number of guards that are sufficient to cover or see every point in the interior of an art gallery. An art gallery can be viewed as a polygon P with or without holes with a total of n vertices and guards as points in P . Any point z ∈ P is said to be visible from a guard g if the line segment joining z and g does not intersect the exterior of P . Usua...
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The Art Gallery Problem (AGP) is one of the classical problems in computational geometry. It asks for the minimum number of guards required to achieve visibility coverage of a given polygon. The AGP is well-known to be NP-hard even in restricted cases. In this paper, we consider the Art Gallery Problem with Fading (AGPF): A polygonal region is to be illuminated with light sources such that ever...
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We consider the problem of covering polygons, without any acute interior angles, using a preferably minimum number of squares. The squares must lie entirely within the polygon. Let P be an arbitrary input polygon, with n vertices, coverable by squares. Let (P) denote the minimum number of squares required to cover P. In the rst part of this paper we show an O(n log n+(P)) time algorithm which p...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2010
ISSN: 0166-218X
DOI: 10.1016/j.dam.2009.12.004