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Colouring perfect planar graphs in parallel

  • Iain A. Stewart
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 344)

Abstract

Our algorithm assumes that the perfect planar graph is presented in the form of a planar drawing. However, this is not strictly necessary, for by [11] the problem of constructing a planar drawing of a planar graph is in NC; in particular, this problem can be solved in O(log2 n) time using O(n) processors on a CREW PRAM.

The original version of this algorithm bypassed the construction of the randomized algorithm, by using a different method of selecting a "nice" set of vertices at which to simultaneously perform α–β interchanges, as in the phase of interchanges in Stage 3. Here, a planar multigraph was constructed with vertices corresponding to the α–β components, with edges joining two vertices if and only if the corresponding α–β components had a common adjacent uncoloured vertex. This multigraph was then coloured using at most 5 colours and our "nice" set of vertices was chosen using this colouring. For more details, see [14]. We are indebted to an anonymous referee for pointing out Luby's technique and thus speeding up the algorithm considerably.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Iain A. Stewart
    • 1
  1. 1.Computing LaboratoryUniversity of Newcastle upon TyneNewcastle upon TyneEngland

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