## Abstract

Augmenting an undirected or a directed graph (digraph) by adding new edges or arcs, to increase its connectivity to a target value, is a fundamental problem in combinatorial optimization and graph theory. In this paper we study the basic problem of augmenting an input digraph to make it strongly connected, which is known as the Strong Connectivity Augmentation problem. Here, the input is a digraph D = (V, A), a set of links L ⊆ V × V, and a positive integer k. The objective is to decide if there exists a subset F ⊆ L, of size at most k, such that D^{0} = (V, A ∪ F) is strongly connected. We consider the general version of this problem where, additionally, there is a weight function w : L → R^{+} on the links, and the goal is to find a minimum weight subset F ⊆ L of cardinality at most k, such that D^{0} = (V, A∪F) is strongly connected. We design an algorithm for this problem that runs in time 2^{O}(k log k)n^{O}^{(1)}, thereby showing that it is fixed parameter tractable (FPT). Here, n = |V |. This also resolves an open problem stated by Guo and Uhlmann more than a decade ago [ Networks 56(2): 131-142 (2010)].

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

Title of host publication | Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms (SODA) |

Editors | Dániel Marx |

Number of pages | 16 |

Publisher | Association for Computing Machinery |

Publication date | 2021 |

Pages | 219-234 |

ISBN (Electronic) | 9781611976465 |

DOIs | |

Publication status | Published - 2021 |

Event | 32nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2021 - Alexandria, Virtual, United States Duration: 10. Jan 2021 → 13. Jan 2021 |

### Conference

Conference | 32nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2021 |
---|---|

Country/Territory | United States |

City | Alexandria, Virtual |

Period | 10/01/2021 → 13/01/2021 |

Sponsor | ACM Special Interest Group on Algorithms and Computation Theory (SIGACT), SIAM Activity Group on Discrete Mathematics |

Series | Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms |
---|

### Bibliographical note

Publisher Copyright:Copyright © 2021 by SIAM