Searching for mobile intruders in circular corridors by two 1-searchers

We consider the problem of searching for a mobile intruder in a circular corridor by two mobile searchers, who hold one flashlight. A circular corridor is a polygon with one polygonal hole such that its outer and inner boundaries are mutually weakly visible. Both 1-searchers always direct their flashlights at the inner boundary. The objective is to decide whether there exists a search schedule   for two 1-searchers to detect the intruder, no matter how fast he moves, and if so, generate a search schedule. We give a characterization of the circular corridors, which are searchable by two 1-searchers. Based on our characterization, an O(nlogn)O(nlogn) time algorithm is then presented to determine the searchability of a circular corridor, where nn denotes the total number of vertices of the outer and inner boundaries. Moreover, a search schedule can be reported in time linear in its size, if it exists.