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

  • Evmorfia Argyriou
  • Sabine Cornelsen
  • Henry FörsterEmail author
  • Michael Kaufmann
  • Martin Nöllenburg
  • Yoshio Okamoto
  • Chrysanthi Raftopoulou
  • Alexander Wolff
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11282)

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.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.yWorks GmbHTübingenGermany
  2. 2.University of KonstanzKonstanzGermany
  3. 3.University of TübingenTübingenGermany
  4. 4.TU WienViennaAustria
  5. 5.RIKEN Center for Advanced Intelligence ProjectUniversity of Electro-CommunicationsChōfuJapan
  6. 6.National Technical University of AthensAthensGreece
  7. 7.University of WürzburgWürzburgGermany

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