LIPIcs.FSTTCS.2022.18.pdf
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Half-Guarding Weakly-Visible Polygons and Terrains
Authors
Ramesh K. Jallu 
,
Erik Krohn ,
- Publication date: 2022-12-14
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Creative Commons Attribution 4.0 International license
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Volume:
42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS)
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Nandhana Duraisamy, Hannah Miller Hillberg, Ramesh K. Jallu, Erik Krohn, Anil Maheshwari, Subhas C. Nandy, and Alex Pahlow. Half-Guarding Weakly-Visible Polygons and Terrains. In 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 250, pp. 18:1-18:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.FSTTCS.2022.18
https://doi.org/10.4230/LIPIcs.FSTTCS.2022.18
Abstract
We consider a variant of the art gallery problem where all guards are limited to seeing 180degree. Guards that can only see in one direction are called half-guards. We give a polynomial time approximation scheme for vertex guarding the vertices of a weakly-visible polygon with half-guards. We extend this to vertex guarding the boundary of a weakly-visible polygon with half-guards. We also show NP-hardness for vertex guarding a weakly-visible polygon with half-guards. Lastly, we show that the orientation of half-guards is critical in terrain guarding. Depending on the orientation of the half-guards, the problem is either very easy (polynomial time solvable) or very hard (NP-hard).
Subject Classification
ACM Subject Classification
- Theory of computation → Approximation algorithms analysis
Keywords
- Art Gallery Problem
- Approximation Algorithm
- NP-Hardness
- Monotone Polygons
- Half-Guards
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References
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