Graph Embedding with Minimum Depth and Maximum External Face

  • Carsten Gutwenger
  • Petra Mutzel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2912)


We present new linear time algorithms using the SPQR-tree data structure for computing planar embeddings of planar graphs optimizing certain distance measures. Experience with orthogonal drawings generated by the topology-shape-metrics approach shows that planar embeddings following these distance measures lead to improved quality of the final drawing in terms of bends, edge length, and drawing area.

Given a planar graph, the algorithms compute the planar embedding with

  1. 1

    the minimum depth among the set of all planar embeddings of G,

  2. 2

    the external face of maximum size among the set of all planar embeddings of G,

  3. 3

    the external face of maximum size among the set of all embeddings of G with minimum depth.



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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Carsten Gutwenger
    • 1
  • Petra Mutzel
    • 2
  1. 1.Stiftung caesarBonnGermany
  2. 2.Vienna University of TechnologyViennaAustria

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