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Algorithmica

, Volume 81, Issue 5, pp 2046–2071 | Cite as

On Smooth Orthogonal and Octilinear Drawings: Relations, Complexity and Kandinsky Drawings

  • Michael A. Bekos
  • Henry FörsterEmail author
  • Michael Kaufmann
Article
  • 25 Downloads

Abstract

We study two variants of the well-known orthogonal graph drawing model: (1) the smooth orthogonal, and (2) the octilinear. Both models are extensions of the orthogonal one, by supporting one additional type of edge segments (circular arcs and diagonal segments, respectively). For planar graphs of maximum vertex degree 4, we analyze relationships between the graph classes that can be drawn bendless in the two models and we also prove \(\mathcal {NP}\)-hardness for a restricted version of the bendless drawing problem for both models. For planar graphs of higher vertex degree, we present an algorithm that produces bi-monotone smooth orthogonal drawings with at most two segments per edge, which also guarantees a linear number of edges with exactly one segment.

Keywords

Graph drawing Smooth orthogonal Octilinear 

Notes

Acknowledgements

This work has been supported by DFG Grant Ka812/17-1. The authors would like to thank Patrizio Angelini and Martin Gronemann for useful discussions. We would also like to thank the anonymous reviewers for useful comments.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Wilhelm-Schickard-Institut für InformatikUniversität TübingenTübingenGermany

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