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International Symposium on Mathematical Foundations of Computer Science

MFCS 1989: Mathematical Foundations of Computer Science 1989 pp 207–217Cite as

Optimal parallel algorithms for the recognition and colouring outerplanar graphs

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 379))

Abstract

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.

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Author information

Authors and Affiliations

  1. Instytut Informatyki, Uniwersytet Warszawski PKiN, p. 850, 00-901, Warszawa, Poland

    Krzysztof Diks & Wojciech Rytter

  2. Fachbereich Informatik, Universität des Saarlandes, D-6600, Saarbrücken, West Germany

    Torben Hagerup

Authors
  1. Krzysztof Diks
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  2. Torben Hagerup
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  3. Wojciech Rytter
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Editor information

Antoni Kreczmar Grazyna Mirkowska

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© 1989 Springer-Verlag Berlin Heidelberg

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Diks, K., Hagerup, T., Rytter, W. (1989). Optimal parallel algorithms for the recognition and colouring outerplanar graphs. In: Kreczmar, A., Mirkowska, G. (eds) Mathematical Foundations of Computer Science 1989. MFCS 1989. Lecture Notes in Computer Science, vol 379. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51486-4_68

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  • DOI: https://doi.org/10.1007/3-540-51486-4_68

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51486-2

  • Online ISBN: 978-3-540-48176-8

  • eBook Packages: Springer Book Archive

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