Abstract
We show that a 5-colouring of the vertices of an n-vertex planar graph may be computed in O(log n log* n) time by an exclusive-read exclusive-write parallel RAM with O(n/(log n log* n)) processors. Our algorithm, while faster than all previously known methods, is at the same time the first parallel 5-colouring algorithm to achieve optimal speedup. It should be emphasized that although input to the algorithm is a planar graph, we do not require a planar embedding to be given as part of the input.
Other results concern the colouring of graphs of bounded genus and the construction of search structures for triangular planar subdivisions.
On leave from Institute of Informatics, Warsaw University.
Supported by the DFG, SFB 124, TP B2, VLSI Entwurfsmethoden und Parallelität.
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© 1987 Springer-Verlag Berlin Heidelberg
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Hagerup, T., Chrobak, M., Diks, K. (1987). Parallel 5-colouring of planar graphs. In: Ottmann, T. (eds) Automata, Languages and Programming. ICALP 1987. Lecture Notes in Computer Science, vol 267. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-18088-5_25
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DOI: https://doi.org/10.1007/3-540-18088-5_25
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