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)

Abstract

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.

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Copyright information

© Springer-Verlag 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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