منابع مشابه
Fast Vertex Guarding for Polygons
For a polygon P with n vertices, the vertex guarding problem asks for the minimum subset G of P ’s vertices such that every point in P is seen by at least one point in G. This problem is NP-complete and APX-hard. The first approximation algorithm (Ghosh, 1987) involves decomposing P into O ( n ) cells that are equivalence classes for visibility from the vertices of P . This discretized problem ...
متن کاملConstant Approximation Algorithms for Guarding Simple Polygons using Vertex Guards
The art gallery problem enquires about the least number of guards sufficient to ensure that an art gallery, represented by a polygon P , is fully guarded. Most standard versions of this problem are known to be NP-hard. In 1987, Ghosh provided a deterministic O(log n)approximation algorithm for the case of vertex guards and edge guards in simple polygons. In the same paper, Ghosh also conjecture...
متن کاملOn k-Guarding Polygons
We describe a polynomial time O(k log log OPTk(P ))approximation algorithm for the k-guarding problem of finding a minimum number, OPTk(P ), of vertex guards of an n-vertex simple polygon P so that for every point p ∈ P , the number of guards that see p is at least the minimum of k and the number of vertices that see p. Our approach finds O ( k ε log log 1 ε ) size (k, ε)-nets for instances of ...
متن کاملVertex Guarding in Weak Visibility Polygons
The art gallery problem enquires about the least number of guards that are sufficient to ensure that an art gallery, represented by a polygon P , is fully guarded. In 1998, the problems of finding the minimum number of point guards, vertex guards, and edge guards required to guard P were shown to be APX-hard by Eidenbenz, Widmayer and Stamm. In 1987, Ghosh presented approximation algorithms for...
متن کاملOn k-Guarding of Polygons
A polygon is called k-guardable if it is possible to find a collection G of points in the interior of the edges of P such that every point in P is visible from at least k elements of G, and such that no edge of P contains more than one element of G. In this paper we prove that every simple polygon can be 1-guarded using at most n/2 guards, and that every polygon with 0 or 1 polygonal hole can...
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ژورنال
عنوان ژورنال: Computational Geometry
سال: 2009
ISSN: 0925-7721
DOI: 10.1016/j.comgeo.2008.07.004