## Abstract

We generalize and unify techniques from several papers to obtain relatively simple and general technique for designing approximation algorithms for finding min-cost k-node connected spanning subgraphs. For the general instance of the problem, the previously best known algorithm has approximation ratio 2k. For k ≤ 5, algorithms with approximation ratio [(k+1)/2] are known. For metric costs Khuller and Raghavachari gave a (2 + 2(k−1)/n)-approximation algorithm. We obtain the following results. (i) An I(k−k_{0})-approximation algorithm for the problem of making a k0-connected graph k-connected by adding a minimum cost edge set, where I(k) = 2+ (eqution found). (ii) A (2 + k−1/n)-approximation algorithm for metric costs. (iv) A [(k + 1)/2]-approximation algorithm for k = 6, 7. (v) A fast [(k + 1)/2]-approximation algorithm for k = 4. The multiroot problem generalizes the min-cost k-connected subgraph problem. In the multiroot problem, requirements k_{u} for every node u are given, and the aim is to find a minimum-cost subgraph that contains max{k_{u}, k_{v}} internally disjoint paths between every pair of nodes u, v. For the general instance of the problem, the best known algorithm has approximation ratio 2k, where k = maxk_{u}. For metric costs there is a 3-approximation algorithm. We consider the case of metric costs, and, using our techniques, improve for k ≤ 7 the approximation guarantee from 3 to 2 + [(k−1)/2]/k < 2.5.

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

Title of host publication | Approximation Algorithms for Combinatorial Optimization - 3rd International Workshop, APPROX 2000, Proceedings |

Editors | Klaus Jansen, Samir Khuller |

Publisher | Springer Verlag |

Pages | 194-205 |

Number of pages | 12 |

ISBN (Electronic) | 9783540679967 |

DOIs | |

State | Published - 2000 |

Event | 3rd International Workshop on Approximation Algorithms for Combinatorial Optimization, APPROX 2000 - Saarbrucken, Germany Duration: 5 Sep 2000 → 8 Sep 2000 |

### Publication series

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

Volume | 1913 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 3rd International Workshop on Approximation Algorithms for Combinatorial Optimization, APPROX 2000 |
---|---|

Country/Territory | Germany |

City | Saarbrucken |

Period | 5/09/00 → 8/09/00 |

### Bibliographical note

Publisher Copyright:© Springer-Verlag Berlin Heidelberg 2000.