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Scandinavian Workshop on Algorithm Theory

SWAT 2000: Algorithm Theory - SWAT 2000 pp 71–82Cite as

A Dynamic Algorithm for Maintaining Graph Partitions

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1851))

Abstract

We propose an algorithm for maintaining a partition of dynamic planar graphs motivated by applications in load balancing for solving partial differential equations on a shared memory multiprocessor. We consider planar graphs of bounded face sizes that can be modified by local insertions or deletions of vertices or edges so that planarity is preserved. In our paper we describe a data structure that can be updated in O(log n) time after any such modification of the graph, where n is the current size of the graph, and allows an almost optimal partition of a required size to be maintained. More precisely, the size of the separator is within an O(n δ) factor of the optimal for the class of planar graphs, where δ is any positive constant, and can be listed in time proportional to its size. The dynamic data structure occupies O(n) space and can initially be constructed in time linear to the size of the original graph.

This work was partially supported by the EPA grant R82-5207-01-0, EPSRC grant GR/M60750, and RTDF grant 98/99-0140. A two-page abstract of this work appeared in the proceedings of CCCG’98.

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References

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Author information

Authors and Affiliations

  1. Center of Informatics, Bulgarian Academy of Sciences, G.Bonchev Str. 25-A, 1113, Sofia, Bulgaria

    Lyudmil G. Aleksandrov

  2. Department of Computer Science, University of Warwick, Coventry, CV4 7AL, UK

    Hristo_N. Djidjev

Authors
  1. Lyudmil G. Aleksandrov
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  2. Hristo_N. Djidjev
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© 2000 Springer-Verlag Berlin Heidelberg

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Aleksandrov, L.G., Djidjev, H. (2000). A Dynamic Algorithm for Maintaining Graph Partitions. In: Algorithm Theory - SWAT 2000. SWAT 2000. Lecture Notes in Computer Science, vol 1851. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44985-X_8

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  • DOI: https://doi.org/10.1007/3-540-44985-X_8

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67690-4

  • Online ISBN: 978-3-540-44985-0

  • eBook Packages: Springer Book Archive

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