Spirality of Orthogonal Representations and Optimal Drawings of Series-Parallel Graphs and 3-Planar Graphs (Extended Abstract)

An orthogonal drawing of a graph is a planar drawing such that all the edges are polygonal chains of horizontal and vertical segments. Finding the planar embedding of a planar graph such that its orthogonal drawing has the minimum number of bends is a fundamental open problem in graph drawing. This paper provides the first partial solution to the problem. It gives a new combinatorial characterization of orthogonal drawings based on the concept of spirality and provides a polynomial-time algorithm for series-parallel graphs and biconnected 3-planar graphs.

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