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arXiv · 2403.18980

A census of graph-drawing algorithms based on generalized transversal structures

Olivier Bernardi·Éric Fusy·Shizhe Liang
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Abstract

We present two graph drawing algorithms based on the recently defined "grand-Schnyder woods", which are a far-reaching generalization of the classical Schnyder woods. The first is a straight-line drawing algorithm for plane graphs with faces of degree 3 and 4 with no separating 3-cycle, while the second is a rectangular drawing algorithm for the dual of such plane graphs. In our algorithms, the coordinates of the vertices are defined in a global manner, based on the underlying grand-Schnyder woods. The grand-Schnyder woods and drawings are computed in linear time. When specializing our algorithms to special classes of plane graphs, we recover the following known algorithms: (1) He's algorithm for rectangular drawing of 3-valent plane graphs, based on transversal structures, (2) Fusy's algorithm for the straight-line drawing of triangulations of the square, based on transversal structures, (3) Bernardi and Fusy's algorithm for the orthogonal drawing of 4-valent plane graphs, based on 2-orientations, (4) Barriere and Huemer's algorithm for the straight-line drawing of quadrangulations, based on separating decompositions. Our contributions therefore provide a unifying perspective on a large family of graph drawing algorithms that were originally defined on different classes of plane graphs and were based on seemingly different combinatorial structures.

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Olivier Bernardi, Éric Fusy, Shizhe Liang. 2025-03-01. A census of graph-drawing algorithms based on generalized transversal structures. https://arxiv.org/abs/2403.18980

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