Path-Width and Three-Dimensional Straight-Line Grid Drawings of Graphs

  • Vida Dujmović
  • Pat Morin
  • David R. Wood
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2528)

Abstract

We prove that every n-vertex graph G with path-width pw(G) has a three-dimensional straight-line grid drawing with O(pw(G)2·n) volume. Thus for graphs with bounded path-width the volume is O(n), and it follows that for graphs with bounded tree-width, such as series-parallel graphs, the volume is O(n log2n). No better bound than O(n2) was previously known for drawings of series-parallel graphs. For planar graphs we obtain three-dimensional drawings with O(n2) volume and O(√n) aspect ratio, whereas all previous constructions with O(n2) volume have Θ(n) aspect ratio.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Vida Dujmović
    • 1
  • Pat Morin
    • 2
  • David R. Wood
    • 2
  1. 1.School of Computer ScienceMcGill UniversityMontréalCanada
  2. 2.School of Computer ScienceCarleton UniversityOttawaCanada

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