  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].
