Worman, Chris; Keil, J. Mark Polygon decomposition and the orthogonal art gallery problem. (English) Zbl 1144.65015 Int. J. Comput. Geom. Appl. 17, No. 2, 105-138 (2007). It is NP-dard to find the minimum number of guards to watch the interior of an \(n\)-wall art gallery. However, if the guards have a restricted form of visibility, the problem may change its complexity. In this paper, the authors consider the problem about \(r\)-visibility. Two points \(p\) and \(q\) are \(r\)-visible if the orthogonal bounding rectangle for \(p\) and \(q\) lies within a given rectilinear polygon \(P\). The authors showed a polynomial-time algorithm to find the minimum number of guards with \(r\)-visibility to watch a rectilinear polygon. Reviewer: Du Ding-Zhu (Richardson) Cited in 3 ReviewsCited in 24 Documents MSC: 65D18 Numerical aspects of computer graphics, image analysis, and computational geometry Keywords:art gallery; polygon decomposition; polygon covering; orthogonal polygons; polynomial-time algorithm PDFBibTeX XMLCite \textit{C. Worman} and \textit{J. M. Keil}, Int. J. Comput. Geom. Appl. 17, No. 2, 105--138 (2007; Zbl 1144.65015) Full Text: DOI References: [1] DOI: 10.1137/1.9780898719796 · Zbl 0919.05001 · doi:10.1137/1.9780898719796 [2] Breen M., Geometri. Ded. 60 pp 283– [3] DOI: 10.1016/0095-8956(85)90049-8 · Zbl 0674.05058 · doi:10.1016/0095-8956(85)90049-8 [4] Garey M. R., Computers and Intractability: A Guide to the Theory of NP-Completeness (1979) · Zbl 0411.68039 [5] Gewali L., Inf. Sci. 7 pp 45– [6] Golumbic M. C., Computer Science and Applied Mathematics, in: Algorithmic Graph Theory and Perfect Graphs (1980) · Zbl 0541.05054 [7] DOI: 10.1007/BF02579273 · Zbl 0492.90056 · doi:10.1007/BF02579273 [8] DOI: 10.1137/0214056 · Zbl 0575.68077 · doi:10.1137/0214056 [9] DOI: 10.1016/B978-044482537-7/50012-7 · doi:10.1016/B978-044482537-7/50012-7 [10] DOI: 10.1016/S0927-0507(05)12008-8 · doi:10.1016/S0927-0507(05)12008-8 [11] Lovász L., J. Combinat. Th. 2 pp 253– [12] DOI: 10.1016/0022-0000(90)90017-F · Zbl 0705.68082 · doi:10.1016/0022-0000(90)90017-F This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.