Orthogonal and Smooth Orthogonal Layouts of 1-Planar Graphs with Low Edge Complexity
Abstract
While orthogonal drawings have a long history, smooth orthogonal drawings have been introduced only recently. So far, only planar drawings or drawings with an arbitrary number of crossings per edge have been studied. Recently, a lot of research effort in graph drawing has been directed towards the study of beyond-planar graphs such as 1-planar graphs, which admit a drawing where each edge is crossed at most once. In this paper, we consider graphs with a fixed embedding. For 1-planar graphs, we present algorithms that yield orthogonal drawings with optimal curve complexity and smooth orthogonal drawings with small curve complexity. For the subclass of outer-1-planar graphs, which can be drawn such that all vertices lie on the outer face, we achieve optimal curve complexity for both, orthogonal and smooth orthogonal drawings.
Keywords
Cite
@article{arxiv.1808.10536,
title = {Orthogonal and Smooth Orthogonal Layouts of 1-Planar Graphs with Low Edge Complexity},
author = {Evmorfia Argyriou and Sabine Cornelsen and Henry Förster and Michael Kaufmann and Martin Nöllenburg and Yoshio Okamoto and Chrysanthi Raftopoulou and Alexander Wolff},
journal= {arXiv preprint arXiv:1808.10536},
year = {2018}
}
Comments
Appears in the Proceedings of the 26th International Symposium on Graph Drawing and Network Visualization (GD 2018)