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k-Level Crossing Minimization Is NP-Hard for Trees

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WALCOM: Algorithms and Computation (WALCOM 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6552))

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Abstract

The k-level crossing minimization problem for graphs has received much interest in the graph drawing literature. In this paper we focus on the special case of trees. We show that the 2-level crossing minimization problem for trees where the order of the vertices on one level is fixed is solvable in quadratic time. We also show that the k-level crossing minimization problem for trees for an arbitrary number of levels is NP-Hard. This result exposes a source of difficulty for algorithm designers that compounds earlier results relating to the 2-level crossing minimization problem for graphs.

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Author information

Authors and Affiliations

  1. Complex & Adaptive Systems Laboratory, University College Dublin, Ireland

    Martin Harrigan

  2. Dept. of Computer Science & Information Systems, University of Limerick, Ireland

    Patrick Healy

Authors
  1. Martin Harrigan
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  2. Patrick Healy
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Editor information

Editors and Affiliations

  1. Department of Architecture and Architectural Engineering, Kyoto University, 615-8540, Nishikyo-ku, Kyoto, Japan

    Naoki Katoh

  2. Department of Computer Science and Engineering, Hauz Khas, Indian Institute of Technology, 11016, New Delhi, India

    Amit Kumar

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Harrigan, M., Healy, P. (2011). k-Level Crossing Minimization Is NP-Hard for Trees. In: Katoh, N., Kumar, A. (eds) WALCOM: Algorithms and Computation. WALCOM 2011. Lecture Notes in Computer Science, vol 6552. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19094-0_9

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  • DOI: https://doi.org/10.1007/978-3-642-19094-0_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-19093-3

  • Online ISBN: 978-3-642-19094-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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