## Abstract

In the survivable network design problem SNDP, the goal is to find a minimum-cost subgraph satisfying certain connectivity requirements. We study the vertex-connectivity variant of SNDP in which the input specifies, for each pair of vertices, a required number of vertex-disjoint paths connecting them. We give the first lower bound on the approximability of SNDP, showing that the problem admits no efficient (formula presented) ratio approximation for any fixed ε > 0 unless NP ⊆ DTIME(n^{polylog(}^{n}^{)}). We also show hardness of approximation results for several important special cases of SNDP, including constant factor hardness for the k-vertex connected spanning subgraph problem (k-VCSS) and for the vertex-connectivity augmentation problem, even when the edge costs are severely restricted.

Original language | English |
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Title of host publication | Approximation Algorithms for Combinatorial Optimization - 5th International Workshop, APPROX 2002, Proceedings |

Editors | Klaus Jansen, Stefano Leonardi, Vijay Vazirani |

Publisher | Springer Verlag |

Pages | 185-199 |

Number of pages | 15 |

ISBN (Print) | 3540441867, 9783540441861 |

DOIs | |

State | Published - 2002 |

Externally published | Yes |

Event | 5th International Workshop On Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2002 - Rome, Italy Duration: 17 Sep 2002 → 21 Sep 2002 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 2462 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 5th International Workshop On Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2002 |
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Country/Territory | Italy |

City | Rome |

Period | 17/09/02 → 21/09/02 |

### Bibliographical note

Publisher Copyright:© Springer-Verlag Berlin Heidelberg 2002.