Complexity of Planar Embeddability of Trees inside Simple Polygons
Computational Geometry
2009-08-28 v1 Computational Complexity
Abstract
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].
Cite
@article{arxiv.0908.4041,
title = {Complexity of Planar Embeddability of Trees inside Simple Polygons},
author = {Alireza Bagheri and Mohammadreza Razzazi},
journal= {arXiv preprint arXiv:0908.4041},
year = {2009}
}