A Graph Reduction Step Preserving Element-Connectivity and Applications

  • Chandra Chekuri
  • Nitish Korula
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5555)


Given an undirected graph G = (V,E) and subset of terminals T ⊆ V, the element-connectivity κ G (u,v) of two terminals u,v ∈ T is the maximum number of u-v paths that are pairwise disjoint in both edges and non-terminals V ∖ T (the paths need not be disjoint in terminals). Element-connectivity is more general than edge-connectivity and less general than vertex-connectivity. Hind and Oellermann [18] gave a graph reduction step that preserves the global element-connectivity of the graph. We show that this step also preserves local connectivity, that is, all the pairwise element-connectivities of the terminals.

We give two applications of the step to connectivity and network design problems: First, we show a polylogarithmic approximation for the problem of packing element-disjoint Steiner forests in general graphs, and an O(1)-approximation in planar graphs. Second, we find a very short and intuitive proof of a spider-decomposition theorem of Chuzhoy and Khanna [10] in the context of the single-sink k-vertex-connectivity problem. Our results highlight the effectiveness of the element-connectivity reduction step; we believe it will find more applications in the future.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Chandra Chekuri
    • 1
  • Nitish Korula
    • 1
  1. 1.Dept. of Computer ScienceUniversity of IllinoisUrbanaUSA

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