k-Level Crossing Minimization Is NP-Hard for Trees

  • Martin Harrigan
  • Patrick Healy
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6552)


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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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Martin Harrigan
    • 1
  • Patrick Healy
    • 2
  1. 1.Complex & Adaptive Systems LaboratoryUniversity College DublinIreland
  2. 2.Dept. of Computer Science & Information SystemsUniversity of LimerickIreland

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