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Algorithmica

, Volume 72, Issue 4, pp 1033–1054 | Cite as

A Linear-Time Algorithm for Testing Outer-1-Planarity

  • Seok-Hee HongEmail author
  • Peter Eades
  • Naoki Katoh
  • Giuseppe Liotta
  • Pascal Schweitzer
  • Yusuke Suzuki
Article

Abstract

A graph is 1-planar if it can be embedded in the plane with at most one crossing per edge. It is known that the problem of testing 1-planarity of a graph is NP-complete. In this paper, we study outer-1-planar graphs. A graph is outer-1-planar if it has an embedding in which every vertex is on the outer face and each edge has at most one crossing. We present a linear time algorithm to test whether a given graph is outer-1-planar. The algorithm can be used to produce an outer-1-planar embedding in linear time if it exists.

Keywords

Graph drawing 1-Planar graphs Outer 1-planar graphs 1-Planarity 1-Planar embedding 

Notes

Acknowledgments

This research arose at the Port Douglas Workshop on Geometric Graph Theory, June, 2011, in Australia. The workshop was supported by the IPDF funding from the University of Sydney. Hong was partly supported by her ARC (Australian Research Council) Future Fellowship (FT3), Algorithmics for Visual Analytics of Massive Complex Networks. Liotta was partly supported by MIUR project AMANDA (Algorithmics for MAssive and Networked DAta).

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Seok-Hee Hong
    • 1
    Email author
  • Peter Eades
    • 1
  • Naoki Katoh
    • 2
  • Giuseppe Liotta
    • 3
  • Pascal Schweitzer
    • 4
  • Yusuke Suzuki
    • 5
  1. 1.University of SydneySydneyAustralia
  2. 2.Kyoto UniversityKyotoJapan
  3. 3.University of PerugiaPerugiaItaly
  4. 4.ETHZurichSwitzerland
  5. 5.Niigata UniversityNiigataJapan

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