, Volume 60, Issue 4, pp 890–937 | Cite as

Finding a Minimum-depth Embedding of a Planar Graph in O(n 4) Time

  • Patrizio Angelini
  • Giuseppe Di BattistaEmail author
  • Maurizio Patrignani


Consider an n-vertex planar graph G. The depth of an embedding Γ of G is the maximum distance of its internal faces from the external one. Several researchers pointed out that the quality of a planar embedding can be measured in terms of its depth. We present an O(n 4)-time algorithm for computing an embedding of G with minimum depth. This bound improves on the best previous bound by an O(nlog n) factor. As a side effect, our algorithm improves the bounds of several algorithms that require the computation of a minimum-depth embedding.

Planar embedding Minimum depth Planar graph Triconnected components 


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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Patrizio Angelini
    • 1
  • Giuseppe Di Battista
    • 1
    Email author
  • Maurizio Patrignani
    • 1
  1. 1.Dipartimento di Informatica e AutomazioneUniversità Roma TreRomeItaly

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