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Efficient Union-Find for planar graphs and other sparse graph classes

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Graph-Theoretic Concepts in Computer Science (WG 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1197))

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Abstract

We solve the Union-Find problem (UF) efficiently for the case the input is restricted to several graph classes, namely partial k-trees for any fixed k, d-dimensional grids for any fixed dimension d and for planar graphs. For the later we develop a technique of decomposing such a graph into small subgraphs, patching, that might be useful for other algorithmic problems on planar graphs, too.

By efficiency we do not only mean “linear time” in a theoretical setting but also a practical reorganization of memory such that a dynamic data structures for UF is allocated consecutively and thus to reduce the amount of page fault produced by UF implementations drastically.

Supported by the IFP “Digitale Filter”.

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Author information

Authors and Affiliations

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

    Jens Gustedt

Authors
  1. Jens Gustedt
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Editor information

Fabrizio d'Amore Paolo Giulio Franciosa Alberto Marchetti-Spaccamela

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© 1997 Springer-Verlag Berlin Heidelberg

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Gustedt, J. (1997). Efficient Union-Find for planar graphs and other sparse graph classes. In: d'Amore, F., Franciosa, P.G., Marchetti-Spaccamela, A. (eds) Graph-Theoretic Concepts in Computer Science. WG 1996. Lecture Notes in Computer Science, vol 1197. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62559-3_16

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  • DOI: https://doi.org/10.1007/3-540-62559-3_16

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62559-9

  • Online ISBN: 978-3-540-68072-7

  • eBook Packages: Springer Book Archive

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