On searchability and LR-visibility of polygons

Imagine that intruders are in a dark polygonal room and move at a finite but unbounded speed, trying to avoid detection. Polygon search problem asks whether a polygon is searchable, i.e., no matter how intruders move, searcher(s) can always detect them. A polygon is LR-visible if there exist two boundary points such that the two polygonal chains divided by them are mutually weakly visible. We explore the relationship between the searchability and LR-visibility of a polygon. Our result can be used as a preprocessing step in designing algorithms related to polygon search.