Complexity of Planar Embeddability of Trees inside Simple Polygons

Details Complexity of Planar Embeddability of Trees inside Simple Polygons Complexity of Planar Embeddability of Trees inside Simple Polygons

2009-08-27

arxiv.org/abs/0908.4041v1

Computer Science

Computational Geometry

Scientific paper

Geometric embedding of graphs in a point set in the plane is a well known problem. In this paper, the complexity of a variant of this problem, where the point set is bounded by a simple polygon, is considered. Given a point set in the plane bounded by a simple polygon and a free tree, we show that deciding whether there is a planar straight-line embedding of the tree on the point set inside the simple polygon is NP-complete. This implies that the straight-line constrained point-set embedding of trees is also NP-complete, which was posed as an open problem in [8].

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