Multiply guarded guards in orthogonal art galleries

We prove a new theorem for orthogonal art galleries in which the guards must guard one another in addition to guarding the polygonal gallery. A set of points G in a polygon Pn is a k-guarded guard set for Pn provided that (i) for every point x in Pn there exists a point w in G such that x is visible from w; and (ii) every point in G is visible from at least k other points in G: The polygon Pn is orthogonal provided each interior angle is 90° or 270°. We prove that for k ≥ 1 and n ≥ 6 every orthogonal polygon with n sides has a k-guarded guard set of cardinality (Formula Presented.) this bound is best possible. This result extends our recent theorem that treats the case k = 1. © Springer-Verlag Berlin Heidelberg 2001.

2 citations (Crossref) [2023-10-31] tex.type: Proceedings paper