Optimal parallel algorithms for the recognition and colouring outerplanar graphs

  • Krzysztof Diks
  • Torben Hagerup
  • Wojciech Rytter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 379)


We show how to test outerplanarity in time T(n)=O(lognlog n) using n/T(n) processors of CREW PRAM. It is the first optimal parallel algorithm recognizing a nontrivial class of graphs and it is the main result of the paper. If the graph is outerplanar and biconnected then a Hamiltonian cycle is produced. Using this cycle and optimal parsing algorithm for bracket expressions the construction of the tree of faces as well as vertex colourings (with the smallest number of colours) are also done by optimal parallel algorithms.


Planar Graph Chromatic Number Hamiltonian Cycle Outerplanar Graph Vertex Colouring 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Krzysztof Diks
    • 1
  • Torben Hagerup
    • 2
  • Wojciech Rytter
    • 1
  1. 1.Instytut InformatykiUniwersytet Warszawski PKiNWarszawaPoland
  2. 2.Fachbereich InformatikUniversität des SaarlandesSaarbrückenWest Germany

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