Clearing a Polygon with Two 1-Searchers

We present an algorithm for a pair of pursuers, each with one flashlight, searching for an unpredictable, moving target in a 2D environment (simple polygon). Given a polygon with n edges and m concave regions, the algorithm decides in time O(n + nm + m) whether the polygon can be cleared by the two 1-searchers, and if so, constructs a search schedule. The pursuers are allowed to move on the boundary and in the interior of the polygon. They are not required to maintain mutual visibility throughout the pursuit.