Searching a room by two guards

Abstract

We consider the problem of searching for mobile intruders in a polygonal region with one door by two guards. Given a simple polygon P with a door d, which is called a room (P, d), two guards start at d and walk along the boundary of P to detect a mobile intruder with a laser beam between the two guards. During the walk, two guards are required to be mutually visible all the time and eventually meet at one point. We give a characterization of the class of rooms searchable by two guards and an O (n log n)-time algorithm to test if a given room admits a walk, where n is the number of the vertices in P.