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Parameterized Complexity of 1-Planarity

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Algorithms and Data Structures (WADS 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8037))

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Abstract

We consider the problem of finding a 1-planar drawing for a general graph, where a 1-planar drawing is a drawing in which each edge participates in at most one crossing. Since this problem is known to be NP-hard we investigate the parameterized complexity of the problem with respect to the vertex cover number, tree-depth, and cyclomatic number. For these parameters we construct fixed-parameter tractable algorithms. However, the problem remains NP-complete for graphs of bounded bandwidth, pathwidth, or treewidth.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of California, Irvine, USA

    Michael J. Bannister & David Eppstein

  2. Faculty of Mathematics and Physics, University of Ljubljana, Slovenia

    Sergio Cabello

Authors
  1. Michael J. Bannister
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  2. Sergio Cabello
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  3. David Eppstein
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Editor information

Editors and Affiliations

  1. School of Computer Science, Parallel Computing and Bioinformatics Laboratory, Carleton University, VISM Building, Room 6210, 1125 Colonel By Drive, K1S 5B6, Ottawa, ON, Canada

    Frank Dehne

  2. Department of Computer Science, The University of Western Ontario, N6A 5B7, London, ON, Canada

    Roberto Solis-Oba

  3. School of Computer Science, Carleton University, K1S 5B6, Ottawa, ON, Canada

    Jörg-Rüdiger Sack

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Bannister, M.J., Cabello, S., Eppstein, D. (2013). Parameterized Complexity of 1-Planarity. In: Dehne, F., Solis-Oba, R., Sack, JR. (eds) Algorithms and Data Structures. WADS 2013. Lecture Notes in Computer Science, vol 8037. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40104-6_9

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  • DOI: https://doi.org/10.1007/978-3-642-40104-6_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40103-9

  • Online ISBN: 978-3-642-40104-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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