Rectilinear Planar Layouts of Planar Graphs and Bipolar Orientations

Abstract:

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 co-ordinates. The total space occupied by the layout is at most n 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 algorithmis based on the concept of a bipolar orientation. We discuss relationships among the bipolar orientations
of a planar graph.