Elsevier

Pattern Recognition Letters

Volume 14, Issue 9, September 1993, Pages 727-732
Pattern Recognition Letters

An art gallery theorem for line segments in the plane

https://doi.org/10.1016/0167-8655(93)90143-2Get rights and content

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 pl on one of the segments in S which sees every point of l. That is, for any point p on segment l the segment plp does not intersect the interior of any line segment other than those containing p and pl. 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.

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There are more references available in the full text version of this article.

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