Norman Do Art Gallery Theorems
نویسندگان
چکیده
Imagine that you are the owner of several art galleries and that you are in the process of hiring people to guard one of them. Unfortunately, with so many in your possession, you seem to have forgotten the exact shape of this particular one. In fact, all you can remember is that the art gallery is a polygon with n sides. Of course, guards have the capacity to turn around a full 360◦ and can see everything in their line of sight, but being terribly unfit, they are unwilling to move. The question we would like to answer is the following.
منابع مشابه
Art Gallery Theorems and Algorithms the International Series of Monographs on Computer Science Editors
متن کامل
The Inapproximability of Illuminating Polygons by α-Floodlights
We consider variants of the art gallery problem where guard visibility is limited to a certain angular aperture α. We show that the problem is NP-hard even when guards can be located in the interior of the polygon. We then proceed to prove that both this problem and its vertex variant, where guard placement is restricted to the vertices of the polygon, are APX-hard. We observe that earlier cons...
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 کاملArt 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 کاملArt Galleries, Fortresses, and Prison Yards: Illumination and Color
An art gallery problem asks for the minimum number of guards needed to protect a given geometric object such as a polygon or polyhedron. We emphasize results obtained using coloring arguments graphs. We also introduce a new technique (same-sign graphs) that simplifies the proofs of several known theorems. – This talk is accessible for graduate students in all areas of math, as well as advanced ...
متن کامل