2009/08/27 by Alireza Bagheri, Bagheri, Alireza, Mohammadreza Razzazi +1
Computer Science · Engineering · #Computational Geometry and Mesh Generation #Advanced Graph Theory Research #3D Modeling in Geospatial Applications
paper · pdf · doi:10.48550/arxiv.0908.4041
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].