An art gallery theorem for line segments in the plane

Abstract Given a set L of n non-intersecting line segments in the plane, we show that it is possible to choose a set S of at most ⌞n/2⌟ segments such that for each segment l of L there exists a point p l on one of the segments in S which sees every point of l . That is, for any point p on segment l the segment p l p does not intersect the interior of any line segment other than those containing p and p l . This bound is also shown to be tight. Thus, by imagining that each segment of S contains an edge guard, we conclude that ⌞n/2⌟ edge guards are sometimes necessary and always sufficient to guard any set of n segments in the plane.