The Contiguous Art Gallery Problem is Solvable in Polynomial Time
I tiakina i:
| I whakaputaina i: | arXiv.org (Dec 18, 2024), p. n/a |
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| Kaituhi matua: | |
| Ētahi atu kaituhi: | , , |
| I whakaputaina: |
Cornell University Library, arXiv.org
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| Ngā marau: | |
| Urunga tuihono: | Citation/Abstract Full text outside of ProQuest |
| Ngā Tūtohu: |
Kāore He Tūtohu, Me noho koe te mea tuatahi ki te tūtohu i tēnei pūkete!
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MARC
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|---|---|---|---|
| 001 | 3147264975 | ||
| 003 | UK-CbPIL | ||
| 022 | |a 2331-8422 | ||
| 035 | |a 3147264975 | ||
| 045 | 0 | |b d20241218 | |
| 100 | 1 | |a Magnus Christian Ring Merrild | |
| 245 | 1 | |a The Contiguous Art Gallery Problem is Solvable in Polynomial Time | |
| 260 | |b Cornell University Library, arXiv.org |c Dec 18, 2024 | ||
| 513 | |a Working Paper | ||
| 520 | 3 | |a In this paper, we study the Contiguous Art Gallery Problem, introduced by Thomas C. Shermer at the 2024 Canadian Conference on Computational Geometry, a variant of the classical art gallery problem from 1973 by Victor Klee. In the contiguous variant, the input is a simple polygon \(P\), and the goal is to partition the boundary into a minimum number of polygonal chains such that each chain is visible to a guard. We present a polynomial-time real RAM algorithm, which solves the contiguous art gallery problem. Our algorithm is simple and practical, and we make a C++ implementation available. In contrast, many variations of the art gallery problem are at least NP-hard, making the contiguous variant stand out. These include the edge-covering problem, proven NP-hard by Laurentini [The Visual Computer 1999], and the classical art gallery problem, recently shown \(\exists\mathbb{R}\)-complete by Abrahamsen, Adamaszek, and Miltzow [J. ACM 2022]. Our algorithm is a greedy algorithm that repeatedly traverses the polygon's boundary. To find an optimal solution, we show that it is sufficient to traverse the polygon polynomially many times, resulting in a runtime of \(\mathcal{O}\!\left( n^7 \log n \right)\). Additionally, we provide algorithms for the restricted settings, where either the endpoints of the polygonal chains or the guards must coincide with the vertices of the polygon. | |
| 653 | |a Apexes | ||
| 653 | |a Algorithms | ||
| 653 | |a Polygons | ||
| 653 | |a Computational geometry | ||
| 653 | |a Polynomials | ||
| 653 | |a Art galleries & museums | ||
| 653 | |a Greedy algorithms | ||
| 653 | |a Run time (computers) | ||
| 700 | 1 | |a Casper Moldrup Rysgaard | |
| 700 | 1 | |a Jens Kristian Refsgaard Schou | |
| 700 | 1 | |a Svenning, Rolf | |
| 773 | 0 | |t arXiv.org |g (Dec 18, 2024), p. n/a | |
| 786 | 0 | |d ProQuest |t Engineering Database | |
| 856 | 4 | 1 | |3 Citation/Abstract |u https://www.proquest.com/docview/3147264975/abstract/embedded/ZKJTFFSVAI7CB62C?source=fedsrch |
| 856 | 4 | 0 | |3 Full text outside of ProQuest |u http://arxiv.org/abs/2412.13938 |