منابع مشابه
Art Gallery and Illumination Problems
How many guards are necessary, and how many are sufficient to patrol the paintings and works of art in an art gallery with n walls? This wonderfully na¨ıve question of combinatorial geometry has, since its formulation, stimulated an increasing number of of papers and surveys. In 1987, J. O'Rourke published his book Art Gallery Theorems and Algorithms which has further fueled this area of resear...
متن کاملInapproximability of some art gallery problems
We prove that the three art gallery problems Vertex Guard, Edge Guard and Point Guard for simple polygons with holes cannot be approximated by any polynomial time algorithm with a ratio of 1? 28 ln n, for any > 0, unless N P T IM E(n O(log log n)). We obtain our results by extending and modifying the concepts of a construction introduced in Eide98].
متن کاملParameterized Hardness of Art Gallery Problems
Given a simple polygon P on n vertices, two points x, y in P are said to be visible to each other if the line segment between x and y is contained in P. The Point Guard Art Gallery problem asks for a minimum set S such that every point in P is visible from a point in S. The Vertex Guard Art Gallery problem asks for such a set S subset of the vertices of P. A point in the set S is referred to as...
متن کاملFast 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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ژورنال
عنوان ژورنال: Algorithmica
سال: 2014
ISSN: 0178-4617,1432-0541
DOI: 10.1007/s00453-014-9961-x