Three-dimensional graph drawing

  • Robert F. Cohen
  • Peter Eades
  • Tao Lin
  • Frank Ruskey
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 894)


Graph drawing research has been mostly oriented toward two-dimensional drawings. This paper describes an investigation of fundamental aspects of three-dimensional graph drawing. In particular we give three results concerning the space required for three-dimensional drawings.

We show how to produce a grid drawing of an arbitrary n-vertex graph with all vertices located at integer grid points, in an nx2nx2n grid, such that no pair of edges cross. This grid size is optimal to within a constant. We also show how to convert an orthogonal two-dimensional drawing in a H x V integer grid to a three-dimensional drawing with [√H] x [√H] x V volume. Using this technique we show, for example, that three-dimensional drawings of binary trees can be computed with volume [√n] x [√n] x [log n]. We give an algorithm for producing drawings of rooted trees in which the z coordinate of a node represents the depth of the node in the tree; our algorithm minimizes the footprint of the drawing, that is, the size of the projection in the xy plane.

Finally, we list significant unsolved problems in algorithms for three-dimensional graph drawing.


Planar Graph Rooted Tree Binary Tree Edge Crossing Classical Convention 
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 1995

Authors and Affiliations

  • Robert F. Cohen
    • 1
  • Peter Eades
    • 1
  • Tao Lin
    • 2
  • Frank Ruskey
    • 3
  1. 1.Department of Computer ScienceUniversity of NewcastleCallaghanAustralia
  2. 2.CSIRO DITCanberraAustralia
  3. 3.Department of Computer ScienceUniversity of VictoriaVictoriaCanada

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