### Abstract

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 language | English (US) |
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Title of host publication | Automata, Languages and Programming - 36th International Colloquium, ICALP 2009, Proceedings |

Pages | 254-265 |

Number of pages | 12 |

Edition | PART 1 |

DOIs | |

State | Published - Nov 12 2009 |

Event | 36th International Colloquium on Automata, Languages and Programming, ICALP 2009 - Rhodes, Greece Duration: Jul 5 2009 → Jul 12 2009 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Number | PART 1 |

Volume | 5555 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 36th International Colloquium on Automata, Languages and Programming, ICALP 2009 |
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Country | Greece |

City | Rhodes |

Period | 7/5/09 → 7/12/09 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Automata, Languages and Programming - 36th International Colloquium, ICALP 2009, Proceedings*(PART 1 ed., pp. 254-265). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5555 LNCS, No. PART 1). https://doi.org/10.1007/978-3-642-02927-1_22