Tight bounds for the number of edge guards for spiral polygons (Q1339794)

A spiral polygon is a simple polygon with at most one consecutive sequence of reflex vertices. A guard \(g\) is a point in a simple polygon \(P\) that guards all points \(q\) for which the line segment \(\overline {gq} \subseteq P\). An edge guard is a point that translates along an edge, and it guards all points that are guarded by some point on the edge. The paper shows that for spiral polygons with \(n\) vertices in total, \(\lfloor (n + 2)/5\rfloor\) edge guards are sometimes necessary and always sufficient to guard the whole polygon. \textit{J. O'Rourke} [`Art gallery theorems and algorithms' (1987; Zbl 0653.52001)] is the standard reference work on guarding, and a recent overview of many variations on guarding problems and solutions is given by \textit{T. Shermer} [Proc. IEEE 80, 1384-1399 (1992)].