Rectilinear planar layouts and bipolar orientations of planar graphs
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- Rosenstiehl, P. & Tarjan, R.E. Discrete Comput Geom (1986) 1: 343. doi:10.1007/BF02187706
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We propose a linear-time algorithm for generating a planar layout of a planar graph. Each vertex is represented by a horizontal line segment and each edge by a vertical line segment. All endpoints of the segments have integer coordinates. The total space occupied by the layout is at mostn by at most 2n–4. Our algorithm, a variant of one by Otten and van Wijk, generally produces a more compact layout than theirs and allows the dual of the graph to be laid out in an interlocking way. The algorithm is based on the concept of abipolar orientation. We discuss relationships among the bipolar orientations of a planar graph.