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

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.