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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© 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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