On r-Guarding SCOTs – A New Family of Orthogonal Polygons

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Abstract

We define a new family of orthogonal polygons, the SCOTs, which are made up of rectangular rooms linked by rectangular corridors, mimicking properties of real-world buildings. We prove that, if a SCOT P is simple or r-independent, meaning that the extensions of all pairs of adjacent corridors with the same direction are either coincident or disjoint, a minimum-cardinality guard set for guarding P under r-visibility can be computed in polynomial time. To this end, we propose three methods: a linear-time algorithm for simple SCOTs, for both vertex- or point-guards; an O(cc) -time algorithm for an r-independent SCOT with c corridors for vertex-guards; and another one running in time O(c3log c) for point-guards in an r-independent SCOT. For SCOTs with holes and not r-independent, we show that the problem becomes NP -hard – proving that the decision problem is NP -complete for the case of point-guards.

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APA

Cruz, V., & Tomás, A. P. (2022). On r-Guarding SCOTs – A New Family of Orthogonal Polygons. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 13568 LNCS, pp. 713–729). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-20624-5_43

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