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Minimum spanning trees for minor-closed graph classes in parallel

  • Algorithms and Data Structures IV
  • Conference paper
  • First Online:
STACS 98 (STACS 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1373))

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Abstract

For each minor-closed graph class we show that a simple variant of Borůvka's algorithm computes a MST for any input graph belonging to that class with linear costs. Among minor-closed graph classes are e.g planar graphs, graphs of bounded genus, partial k-trees for fixed k, and linkless or knotless embedable graphs. The algorithm can be implemented on a CRCW PRAM to run in logarithmic time with a work load that is linear in the size of the graph. We develop a new technique to find multiple edges in such a graph that might have applications in other parallel reduction algorithms as well.

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Authors and Affiliations

  1. TU Berlin, Sekr. MA 6-1, D-10623, Berlin, Germany

    Jens Gustedt

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  1. Jens Gustedt
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Michel Morvan Christoph Meinel Daniel Krob

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© 1998 Springer-Verlag

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Gustedt, J. (1998). Minimum spanning trees for minor-closed graph classes in parallel. In: Morvan, M., Meinel, C., Krob, D. (eds) STACS 98. STACS 1998. Lecture Notes in Computer Science, vol 1373. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028578

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  • DOI: https://doi.org/10.1007/BFb0028578

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64230-5

  • Online ISBN: 978-3-540-69705-3

  • eBook Packages: Springer Book Archive

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