  A straight-line drawing $\delta$ of a planar graph $G$ need not be plane, but
can be made so by moving some of the vertices. Let shift$(G,\delta)$ denote the
minimum number of vertices that need to be moved to turn $\delta$ into a plane
drawing of $G$. We show that shift$(G,\delta)$ is NP-hard to compute and to
approximate, and we give explicit bounds on shift$(G,\delta)$ when $G$ is a
tree or a general planar graph. Our hardness results extend to
1BendPointSetEmbeddability, a well-known graph-drawing problem.
