Drawing Unordered Trees on k-Grids

  • Christian Bachmaier
  • Marco Matzeder
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7157)


We present almost linear area bounds for drawing complete trees on the octagonal grid. For 7-ary trees we establish an upper and lower bound of Θ(n 1.129) and for ternary trees the bounds of \(\O(n^{1.048})\) and Θ(n), where the latter needs edge bends. We explore the unit edge length and area complexity of drawing unordered trees on k-grids with k ∈ {4, 6, 8} and generalize the \(\mathcal{NP}\)-hardness results of the orthogonal and hexagonal grid to the octagonal grid.


Binary Tree Bottom Half Outgoing Edge Full Tree Linear Time Algorithm 
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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Christian Bachmaier
    • 1
  • Marco Matzeder
    • 1
  1. 1.University of PassauGermany

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