On computing simple circuits on a set of line segments
SCG '86 Proceedings of the second annual symposium on Computational geometry
The complexity of computing simple circuits in the plane
The complexity of computing simple circuits in the plane
Vision: A Computational Investigation into the Human Representation and Processing of Visual Information
An optimal O(n log n) algorithm for contour reconstruction from rays
SCG '87 Proceedings of the third annual symposium on Computational geometry
Long non-crossing configurations in the plane
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Long Non-Crossing Configurations In The Plane
Fundamenta Informaticae
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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.