Journal ArticleDOI
A simple proof of the rectilinear art gallery theorem
Heikki Mannila,Derick Wood +1 more
TLDR
For a rectilinear art gallery with nwalls at most [n/4] guards are needed to keep the entire art gallery under observation, the authors proved that n/4 guards are sufficient.Abstract:
The Rectilinear Art Gallery Theorem states that for a rectilinear art gallery with nwalls at most [n/4] guards are needed to keep the entire art gallery under observation. There have been two proofs of this result. The first proof depends on the quadrilateralization of the art gallery and is quite complicated. The second proof is direct, yet it depends on a graph-theoretic argument at one crucial point. Our proof, on the other hand, is direct, completely geometrical, and at the same time, simple.read more
Citations
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Journal ArticleDOI
Hiding people in polygons
TL;DR: Borders are established on the maximum size of hidden sets and hidden guard sets in and around polygons, and it is shown that the problem of finding a maximum hidden set is NP-hard.
Proceedings ArticleDOI
Minimally covering a horizontally convex orthogonal polygon
TL;DR: In this paper, time algorithms for the problems of covering a horizontally convex orthogonal polygon with the minimum number of Orthogonal convex polygons and with theminimum number of orthogsonal star-shaped polygons are presented.
Journal ArticleDOI
On covering orthogonal polygons with star-shaped polygons
TL;DR: An O( n ) time algorithm for covering a horizontally convex orthogonal polygon with the minimum number of Orthogonal star-shaped polygons with important applications in robotics and pattern recognition is presented.
Posted Content
Guard Placement For Wireless Localization
TL;DR: This work considers the problem of placing fixed localizers that enable mobile communication devices to prove they belong to a secure region that is defined by the interior of a polygon, and provides upper and lower bounds for this model.
References
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Journal ArticleDOI
A short proof of Chvátal's Watchman Theorem
TL;DR: A short proof of Chvatal's Watchman Theorem using the existence of a three-coloring of a triangulated polygon is given in this article, where it is shown that the color of the triangulation of a polygon can be interpreted as a triangle.
Journal ArticleDOI
Traditional Galleries Require Fewer Watchmen
TL;DR: In this paper, it was shown that if every pair of adjacent sides of the polygon form a right angle then at most $[ n/ 4 ]$ guards are needed, and again this result is best possible.