Searching a Circular Corridor with Three Flashlights

We study the problem of searching a circular corridor with three flashlights, a variation of the 1-searcher problem in a circular corridor. A circular corridor is a polygon with one polygonal hole such that its outer and inner boundaries are mutually weakly visible. A flashlight is considered as a 1-searcher who has a flashlight and can see only along the ray of the flashlight emanating from his position. In the searching process, each 1-searcher can move on the boundary or into the circular corridor, the beam of his flashlight must be irradiated on the inner boundary. This paper proves that a given circular corridor can always be cleared by at most three flashlights (1-searchers), and a search schedule can be reported in O(m) time, where m?n2 denotes the walk instructions reported, and n denotes the total number of vertices of the outer and inner boundaries.