Maximizing the guarded boundary of an Art Gallery is APX-complete
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چکیده
منابع مشابه
Maximizing the Guarded Boundary of an Art Gallery Is APX-Complete
In the Art Gallery problem, given is a polygonal gallery and the goal is to guard the gallery’s interior or walls with a number of guards that must be placed strategically in the interior, on walls or on corners of the gallery. Here we consider a more realistic version: exhibits now have size and may have different costs. Moreover the meaning of guarding is relaxed: we use a new concept, that o...
متن کاملMaximizing the Guarded Boundary of an Art Gallery
In the Art Gallery problem, given is a polygonal gallery and the goal is to guard the gallery’s interior or walls with a number of guards that must be placed strategically in the interior, on walls or on corners of the gallery. Here we consider a more realistic version: exhibits now have size and may have different costs. Moreover the meaning of guarding is relaxed: we use a new concept, that o...
متن کاملMaximizing the Guarded Interior of an Art Gallery
In the Art Gallery problem a polygon is given and the goal is to place as few guards as possible so that the entire area of the polygon is covered. We address a closely related problem: how to place a fixed number of guards on the vertices or the edges of a simple polygon so that the total guarded area inside the polygon is maximized. Recall that an optimization problem is called APX-hard, if t...
متن کاملArt gallery theorems for guarded guards
We prove two art gallery theorems in which the guards must guard one another in addition to the gallery. A set G of points (the guards) in a simple closed polygon (the art gallery) is a guarded guard set provided (i) every point in the polygon is visible to some point in G; and (ii) every point in G is visible to some other point in G. We prove that a polygon with n sides always has a guarded g...
متن کاملThe Art Gallery Problem is $\exists \mathbb{R}$-complete
We prove that the art gallery problem is equivalent under polynomial time reductions to deciding whether a system of polynomial equations over the real numbers has a solution. The art gallery problem is a classical problem in computational geometry, introduced in 1973 by Victor Klee. Given a simple polygon P and an integer k, the goal is to decide if there exists a set G of k guards within P su...
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ژورنال
عنوان ژورنال: Computational Geometry
سال: 2007
ISSN: 0925-7721
DOI: 10.1016/j.comgeo.2006.12.001