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

  • Authors:

  • Patrizio Angelini;Giuseppe Di Battista;Maurizio Patrignani

  • Affiliations:

  • Università Roma Tre, Dipartimento di Informatica e Automazione, Rome, Italy;Università Roma Tre, Dipartimento di Informatica e Automazione, Rome, Italy;Università Roma Tre, Dipartimento di Informatica e Automazione, Rome, Italy

  • Venue:
  • Algorithmica
  • Year:
  • 2011

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Abstract

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.