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Computational complexity of art gallery problems
IEEE Transactions on Information Theory, 1986 Summary: We study the computational complexity of the art gallery problem originally posed by Klee, and its variations. Specifically, the problem of determining the minimum number of vertex guards that can see an n-wall simply connected art gallery is shown to be NP-hard.
D. T. Lee, Arthur K. Lin
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NP-completeness of chromatic orthogonal art gallery problem
Journal of Supercomputing, 2020The chromatic orthogonal art gallery problem is a well-known problem in the computational geometry. Two points in an orthogonal polygon P see each other if there is an axis-aligned rectangle inside P contains them. An orthogonal guarding of P is k-colorable, if there is an assignment between k colors and the guards such that the visibility regions of ...
Hamid Hoorfar +2 more
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Art gallery problem with guards whose range of vision is 180∘
Computational Geometry: Theory and Applications, 2000 It is shown that in any polygonal art gallery of n sides it is possible to place ⌊n/3 ⌋ point guards whose range of vision is 180 ◦ so that every interior point of the gallery can be seen by at least one of them.
Csaba D Tóth
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An IP solution to the art gallery problem
Proceedings of the twenty-fifth annual symposium on Computational geometry, 2009The Art Gallery problem (AGP) consists of minimizing the number of guards required to cover a gallery whose boundary is a simple polygon P . In this paper, we describe an Integer Programming based solution to agp that is presented in the accompanying video.
Marcelo C. Couto +2 more
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POLYGON DECOMPOSITION AND THE ORTHOGONAL ART GALLERY PROBLEM
International Journal of Computational Geometry & Applications, 2007A decomposition of a polygon P is a set of polygons whose geometric union is exactly P. We study a polygon decomposition problem that is equivalent to the Orthogonal Art Gallery problem. Two points are r-visible if the orthogonal bounding rectangle for p and q lies within P.
Chris Worman, J. Mark Keil
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The Art Gallery Theorem for Polyominoes [PDF]
Discrete and Computational Geometry, 2012 We explore the art gallery problem for the special case that the domain (gallery) P is an m-polyomino, a polyform whose cells are m unit squares. We study the combinatorics of guarding polyominoes in terms of the parameter m, in contrast with the ...
Thérèse Biedl +2 more
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Tight bounds for the rectangular art gallery problem
1992Consider a rectangular art gallery, subdivided into n rectangular rooms; any two adjacent rooms have a door connecting them. We show that ⌈n/2⌋ guards are always sufficient to protect all rooms in a rectangular art gallery; furthermore, their positioning can be determined in O(n) time.
Jurek Czyzowicz +4 more
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On the rectilinear art gallery problem algorithmic aspects
1991We investigate the watchman problem for rectilinear art galleries with an arbitrary number of holes. An efficient algorithm for the placement of the guards with running time O(n3/2 log2n log log n) is presented. Each guard has to watch an r-star of constant size.
Frank Hoffmann 0002 +1 more
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Effectiveness of Local Search for Art Gallery Problems
2017We study the variant of the art gallery problem where we are given an orthogonal polygon P (possibly with holes) and we want to guard it with the minimum number of sliding cameras. A sliding camera travels back and forth along an orthogonal line segment s in P and a point p in P is said to be visible to the segment s if the perpendicular from p onto s ...
Sayan Bandyapadhyay, Aniket Basu Roy
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