## Abstract

We consider the directed Rooted Subset k -Edge-Connectivity problem: given a digraph G= (V, E) with edge costs, a set T⊂ V of terminals, a root node r, and an integer k, find a min-cost subgraph of G that contains k edge disjoint rt-paths for all t∈ T. The case when every edge of positive cost has head in T admits a polynomial time algorithm due to Frank [9], and the case when all positive cost edges are incident to r is equivalent to the k -Multicover problem. Recently, Chan et al. [2] obtained ratio O(ln kln | T| ) for quasi-bipartite instances, when every edge in G has an end (tail and/or head) in T+ r. We give a simple proof for the same ratio for a more general problem of covering an arbitrary T-intersecting supermodular set function by a minimum cost edge set, and for the case when only every positive cost edge has an end in T+ r.

Original language | English |
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Title of host publication | Computer Science – Theory and Applications - 16th International Computer Science Symposium in Russia, CSR 2021, Proceedings |

Editors | Rahul Santhanam, Daniil Musatov |

Publisher | Springer Science and Business Media Deutschland GmbH |

Pages | 339-348 |

Number of pages | 10 |

ISBN (Print) | 9783030794156 |

DOIs | |

State | Published - 2021 |

Event | 16th International Computer Science Symposium in Russia, CSR 2021 - Sochi, Russian Federation Duration: 28 Jun 2021 → 2 Jul 2021 |

### 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 | 12730 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 16th International Computer Science Symposium in Russia, CSR 2021 |
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Country/Territory | Russian Federation |

City | Sochi |

Period | 28/06/21 → 2/07/21 |

### Bibliographical note

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