Characterization of rooms searchable 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 one 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 the characterization of the class of rooms searchable by two guards, which naturally leads to O(n log n)-time algorithm for testing the searchability of an n-sided room.