O(n2) algorithms for graph planarization

  • R. Jayakumar
  • K. Thulasiraman
  • M. N. S. Swamy
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 344)


In this paper we present two O(n2) planarization algorithms—PLANARIZE and MAXIMAL-PLANARIZE. These algorithms are based on Lempel, Even, and Cederbaum's planarity testing algorithm [9] and its implementation using PQ-trees [8, 13]. Algorithm PLANARIZE is for the construction of a spanning planar subgraph of an n-vertex nonplanar graph. This algorithm proceeds by embedding one vertex at a time and, at each step, adds the maximum number of edges possible without creating nonplanarity of the resultant graph. Given a biconnected spanning planar subgraph Gp of a nonplanar graph G, algorithm MAXIMAL-PLANARIZE constructs a maximal planar subgraph of G which contains Gp. This latter algorithm can also be used to maximally planarize a biconnected planar graph.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • R. Jayakumar
    • 1
  • K. Thulasiraman
    • 1
  • M. N. S. Swamy
    • 1
  1. 1.Faculty of Engineering and Computer ScienceConcordia UniversityMontrealCanada

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