A graph reduction step preserving element-connectivity and applications

Chandra Chekuri, Nitish Korula

Research output: Chapter in Book/Report/Conference proceedingConference contribution


Given an undirected graph G=(V,E) and subset of terminals T⊆V, the element-connectivity κ́ 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.

Original languageEnglish (US)
Title of host publicationAutomata, Languages and Programming - 36th International Colloquium, ICALP 2009, Proceedings
Number of pages12
EditionPART 1
StatePublished - 2009
Event36th International Colloquium on Automata, Languages and Programming, ICALP 2009 - Rhodes, Greece
Duration: Jul 5 2009Jul 12 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 1
Volume5555 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other36th International Colloquium on Automata, Languages and Programming, ICALP 2009

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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