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

Extended abstract
  • Jens Gustedt
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1197)


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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Jens Gustedt
    • 1
  1. 1.TU BerlinBerlinGermany

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