## Abstract

We design exact algorithms for the following two problems in survivable network design: (i) designing a minimum cost network with a desired value of edge connectivity, which is called Minimum Weightλ-connected Spanning Subgraph and (ii) augmenting a given network to a desired value of edge connectivity at a minimum cost which is called Minimum Weightλ-connectivity Augmentation. It is easy to see that a minimum solution to these problems contains at most 2 λ(n- 1) edges. Using this fact one can design a brute-force algorithm which runs in time 2 ^{O}^{(}^{λ}^{n}^{log}^{n}^{)}, however no better algorithms were known previously. In this paper, we give the first single exponential time algorithm for these problems, i.e. running in time 2 ^{O}^{(}^{λ}^{n}^{)}, for both undirected and directed networks. Our results are obtained via well known characterizations of λ-connected graphs, their connections to linear matroids and the recently developed technique of dynamic programming with representative sets.

Original language | English |
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Pages (from-to) | 2622-2641 |

Number of pages | 20 |

Journal | Algorithmica |

Volume | 84 |

Issue number | 9 |

DOIs | |

State | Published - 1 Sep 2022 |

Externally published | Yes |

## Keywords

- Exact algorithms
- Network augmentation
- Survivable network design

## ASJC Scopus subject areas

- General Computer Science
- Computer Science Applications
- Applied Mathematics