Drawing Ordered (k − 1)–Ary Trees on k–Grids

  • Wolfgang Brunner
  • Marco Matzeder
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6502)


We explore the complexity of drawing ordered (k − 1)–ary trees on grids with k directions for \(k \in \left\{4,6,8\right\}\) and within a given area. This includes, e.g., ternary trees drawn on the orthogonal grid. For aesthetically pleasing tree drawings on these grids, we additionally present various restrictions similar to the common hierarchical case. First, we generalize the \({\mathcal{NP}}\)–hardness of minimal width in hierarchical drawings of ordered trees to (k − 1)–ary trees on k–grids and then we generalize the Reingold and Tilford algorithm to k–grids.


Binary Tree Outgoing Edge Minimal Width Boolean Expression Incoming Edge 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Wolfgang Brunner
    • 1
  • Marco Matzeder
    • 1
  1. 1.University of PassauPassauGermany

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