Orthogonal and Smooth Orthogonal Layouts of 1-Planar Graphs with Low Edge Complexity

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2018
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Argyriou, Evmorfia
Förster, Henry
Kaufmann, Michael
Nöllenburg, Martin
Okamoto, Yoshio
Raftopoulou, Chrysanthi
Wolff, Alexander
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BIEDL, Therese, ed., Andreas KERREN, ed.. Graph Drawing and Network Visualization : 26th International Symposium, GD 2018, Proceedings. Cham: Springer, 2018, pp. 509-523. Lecture Notes in Computer Science. 11282. ISSN 0302-9743. eISSN 1611-3349. ISBN 978-3-030-04413-8. Available under: doi: 10.1007/978-3-030-04414-5_36
Zusammenfassung

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.

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Graph Drawing and Network Visualization : 26th International Symposium, GD 2018, 26. Sept. 2018 - 28. Sept. 2018, Barcelona, Spain
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ISO 690ARGYRIOU, Evmorfia, Sabine CORNELSEN, Henry FÖRSTER, Michael KAUFMANN, Martin NÖLLENBURG, Yoshio OKAMOTO, Chrysanthi RAFTOPOULOU, Alexander WOLFF, 2018. Orthogonal and Smooth Orthogonal Layouts of 1-Planar Graphs with Low Edge Complexity. Graph Drawing and Network Visualization : 26th International Symposium, GD 2018. Barcelona, Spain, 26. Sept. 2018 - 28. Sept. 2018. In: BIEDL, Therese, ed., Andreas KERREN, ed.. Graph Drawing and Network Visualization : 26th International Symposium, GD 2018, Proceedings. Cham: Springer, 2018, pp. 509-523. Lecture Notes in Computer Science. 11282. ISSN 0302-9743. eISSN 1611-3349. ISBN 978-3-030-04413-8. Available under: doi: 10.1007/978-3-030-04414-5_36
BibTex
@inproceedings{Argyriou2018-12-18Ortho-44789,
  year={2018},
  doi={10.1007/978-3-030-04414-5_36},
  title={Orthogonal and Smooth Orthogonal Layouts of 1-Planar Graphs with Low Edge Complexity},
  number={11282},
  isbn={978-3-030-04413-8},
  issn={0302-9743},
  publisher={Springer},
  address={Cham},
  series={Lecture Notes in Computer Science},
  booktitle={Graph Drawing and Network Visualization : 26th International Symposium, GD 2018, Proceedings},
  pages={509--523},
  editor={Biedl, Therese and Kerren, Andreas},
  author={Argyriou, Evmorfia and Cornelsen, Sabine and Förster, Henry and Kaufmann, Michael and Nöllenburg, Martin and Okamoto, Yoshio and Raftopoulou, Chrysanthi and Wolff, Alexander}
}
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