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Incremental Maintenance of the 5-Edge-Connectivity Classes of a Graph

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Algorithm Theory - SWAT 2000 (SWAT 2000)

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

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Abstract

Two vertices of an undirected graph are called k-edge-connected if there exist k edge-disjoint paths between them. The equivalence classes of this relation are called k-edge-connected classes, or k-classes for short. This paper shows how to check whether two vertices belong to the same 5-class of an arbitrary connected graph that is undergoing edge insertions. For this purpose we suggest (i) a full description of the 4-cuts of an arbitrary graph and (ii) a representation of the k-classes, 1 = k = 5, of size linear in n-the number of vertices of the graph; these representations can be constructed in a polynomial time. Using them, we suggest an algorithm for incremental maintenance of the 5-classes. The total time for a sequence of m Edge-Insert updates and q Same-5-Class? queries is O(q + m + n · log2n); the worst-case time per query is O(1).

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Authors and Affiliations

  1. Dept. of Computer Science, Ben-Gurion University, Beer-Sheva, 84105, Israel

    Yefim Dinitz

  2. Dept. of Computer Science, Technion, Haifa, 32000, Israel

    Ronit Nossenson

Authors
  1. Yefim Dinitz
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  2. Ronit Nossenson
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© 2000 Springer-Verlag Berlin Heidelberg

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Dinitz, Y., Nossenson, R. (2000). Incremental Maintenance of the 5-Edge-Connectivity Classes of a Graph. 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_25

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  • DOI: https://doi.org/10.1007/3-540-44985-X_25

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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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