## Abstract

The problem of finding a minimum weight k-vertex connected spanning subgraph in a graph G = (V, E) is considered. For k ≥ 2, this problem is known to be NP-hard. Combining properties of inclusion-minimal k-vertex connected graphs and of k-out-connected graphs (i.e., graphs which contain a vertex from which there exist k internally vertex-disjoint paths to every other vertex), we derive polynomial time algorithm for finding a ([k/2] + 1)-connected subgraph with a weight at most twice the optimum to the original problem. In particular, we obtain a 2-approximation algorithm for the case k = 3 of our problem. This improves the best previously known approximation ratio 3. The complexity of the algorithm is O(|V|^{3}|E|) = O(|V|^{5}).

Original language | English |
---|---|

Pages (from-to) | 21-30 |

Number of pages | 10 |

Journal | Journal of Algorithms |

Volume | 32 |

Issue number | 1 |

DOIs | |

State | Published - 1 Jan 1999 |

## ASJC Scopus subject areas

- Control and Optimization
- Computational Mathematics
- Computational Theory and Mathematics