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).
@InProceedings{duraisamy_et_al:LIPIcs.FSTTCS.2022.18, author = {Duraisamy, Nandhana and Hillberg, Hannah Miller and Jallu, Ramesh K. and Krohn, Erik and Maheshwari, Anil and Nandy, Subhas C. and Pahlow, Alex}, title = {{Half-Guarding Weakly-Visible Polygons and Terrains}}, booktitle = {42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)}, pages = {18:1--18:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-261-7}, ISSN = {1868-8969}, year = {2022}, volume = {250}, editor = {Dawar, Anuj and Guruswami, Venkatesan}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2022.18}, URN = {urn:nbn:de:0030-drops-174103}, doi = {10.4230/LIPIcs.FSTTCS.2022.18}, annote = {Keywords: Art Gallery Problem, Approximation Algorithm, NP-Hardness, Monotone Polygons, Half-Guards} }
Feedback for Dagstuhl Publishing