Finding the Minimum Number of Open-Edge Guards in an Orthogonal Polygon is NP-Hard

Abstract

We study the problem of determining the minimum number of open-edge guards which guard the interior of a given orthogonal polygon with holes. Here, an open-edge guard is a guard which is allowed to be placed along open edges of a polygon, that is, the endpoints of the edge are not taken into account for visibility purpose. It is shown that finding the minimum number of open-edge guards for a given orthogonal polygon with holes is NP-hard.