Searching for a Mobile Intruder in a Polygonal Region

The problem of searching for a mobile intruder in a simple polygon by a single mobile searcher is considered. This paper investigates the capabilities of searchers having different degrees of visibility by introducing the searcher having k flashlights whose visibility is limited to k rays emanating from his position, and the searcher having a point light source who can see in all directions simultaneously. This paper presents necessary and sufficient conditions for a polygon to be searchable by various searchers. The paper also introduces a class of polygons for which the searcher having two flashlights is as capable as the searcher having a point light source, and it gives a simple necessary and sufficient condition for such polygons to be searchable by the searcher having two flashlights. The complexity of generating a search schedule under some of these conditions is also discussed. Many of the results are proved using chord systems that represent the visibility relations among the vertices and edges o...