Complexity of Planar Embeddability of Trees inside Simple Polygons [article]

Alireza Bagheri, Mohammadreza Razzazi
2009 arXiv   pre-print
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
more » ... trees is also NP-complete, which was posed as an open problem in [8].
arXiv:0908.4041v1 fatcat:yzotlcqzuzcjvoroiktsi3q52e