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The art gallery problem is ∃ ℝ-complete
Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing, 2018 The Art Gallery Problem (AGP) is a classic problem in computational geometry, introduced in 1973 by Victor Klee. Given a simple polygon 풫 and an integer k , the goal is to decide if there exists a set G of k guards within 풫 such that
Mikkel Abrahamsen +2 more
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Topological Universality of the Art Gallery Problem
CoRR, 2022 We prove that any compact semi-algebraic set is homeomorphic to the solution space of some art gallery problem. Previous works have established similar universality theorems, but holding only up to homotopy equivalence, rather than homeomorphism, and prior to this work, the existence of art galleries even for simple spaces such as the Möbius strip or ...
Stade, Jack, Tucker-Foltz, Jamie
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An Approximation Algorithm for the Art Gallery Problem [PDF]
CoRR, 2016 25 pages, 4 pages proof ideas, many ...
Bonnet, Edouard, Miltzow, Tillmann
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The Point-Boundary Art Gallery Problem Is ∃ℝ-Hard. [PDF]
We resolve the complexity of the point-boundary variant of the art gallery problem, showing that it is ∃ℝ-complete, meaning that it is equivalent under polynomial time reductions to deciding whether a system of polynomial equations has a real solution.
Stade, Jack
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An Exact and Efficient Algorithm for the Orthogonal Art Gallery Problem [PDF]
Computer Graphics and Image Processing (SIBGRAPI), Proceedings of the Brazilian Symposium on, 2007 Cid C De Souza
exaly +4 more sources
A Practical Algorithm for the Viewpoint Planning of Terrestrial Laser Scanners
Geomatics, 2022 Applications using terrestrial laser scanners (TLS) have been skyrocketing in the past two decades. In a scanning project, the configuration of scans is a critical issue as it has significant effects on the project cost and the quality of the product. In
Fengman Jia, Derek D. Lichti
doaj +1 more source
, 2023 In this thesis, we study a classical problem in computational geometry, the Art Gallery Problem. The Art Gallery Problem originates from the question of what is the minimum number of guards required to see the entire gallery.
Smolíková, Natálie
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Invotek: Jurnal Inovasi Vokasional dan Teknologi, 2020 Tari Topeng Patih is a part of the traditional dance performance art “Wayang Topeng Malangan” with a religious background which grew up around people in Malang City, East Java. Presently, art gallery of Tari Topeng Malangan has been difficult to be found.
Bayu Ramadhani Fajri +2 more
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Lower Bound for Sculpture Garden Problem: Localization of IoT Devices
Applied Sciences, 2023 The purpose of the current study is to investigate a special case of art gallery problem, namely a sculpture garden problem. In this problem, for a given polygon P, the ultimate goal is to place the minimum number of guards (landmarks) to define the ...
Marzieh Eskandari +2 more
doaj +1 more source
Art Gallery Problems for Convex Nested Polygons [PDF]
INFORMS Journal on Computing, 1997 In this article, we study a class of Art Gallery problems that are defined on a pair of convex nested polygons. Polynomial time algorithms are presented for all these problems, by reducing them to the Circle Covering problem, or by relating them to the Minimal Nested Polygon problem.
Joy Bhadury +3 more
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