Abstract
Given a collection of line segments in the plane we would like to connect the segments by their endpoints to construct a simple circuit. (A simple circuit is the boundary of a simple polygon). However, there are collections of line segments where this cannot be done. In this note it is proved that deciding whether a set of line segments admits a simple circuit is NP-complete. Deciding whether a set of horizontal line segments can be connected with horizontal and vertical line segments to construct an orthogonal simple circuit is also shown to be NP-complete.
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