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Drawing Unordered Trees on k-Grids

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

Abstract

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.

Keywords

Binary Tree Bottom Half Outgoing Edge Full Tree Linear Time Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

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

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