Computer Science – Computational Geometry
Scientific paper
2007-06-07
Computer Science
Computational Geometry
This paper has been merged with http://arxiv.org/abs/0709.0170
Scientific paper
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.
Goaoc Xavier
Kratochvil Jan
Okamoto Yoshio
Shin Chan-Su
Wolff Alexander
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