GD 2010: Graph Drawing pp 305-316

# Complexity of Finding Non-Planar Rectilinear Drawings of Graphs

• Ján Maňuch
• Murray Patterson
• Sheung-Hung Poon
• Chris Thachuk
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6502)

## Abstract

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 directions are “horizontal” or “vertical” or a cyclic order of the edges at each vertex is specified, the problem is NP-complete. We show that these two NP-complete cases are fixed parameter tractable in the number of vertices of degree 3 or 4.

## Keywords

Minimum Area Input Graph Internal Vertex Truth Assignment Variable Line
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Authors and Affiliations

• Ján Maňuch
• 1
• 2
• Murray Patterson
• 1
• Sheung-Hung Poon
• 3
• Chris Thachuk
• 1
1. 1.Dept. of Computer ScienceUniversity of British ColumbiaVancouverCanada
2. 2.Dept. of MathematicsSimon Fraser UniversityBurnabyCanada
3. 3.Dept. of Computer ScienceNational Tsing Hua UniversityTaiwan, R.O.C.