Complexity of Finding Non-Planar Rectilinear Drawings of Graphs

@inproceedings{Manuch2010ComplexityOF,
  title={Complexity of Finding Non-Planar Rectilinear Drawings of Graphs},
  author={J{\'a}n Manuch and Murray D. Patterson and Sheung-Hung Poon and Chris Thachuk},
  booktitle={Graph Drawing},
  year={2010}
}
We study the complexity of the problem of finding non-planar rectilinear drawings of graphs. This problem is known to be NP-complete. We consider natural restrictions of this problem where constraints are placed on the possible orientations of edges. In particular, we show that if each edge has prescribed direction "left", "right", "down" or "up", the problem of finding a rectilinear drawing is polynomial, while finding such a drawing with the minimum area is NP-complete. When assigned… 

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