### Abstract

In this paper, we consider two location problems of determining the best location of roots of arc-disjoint arborescences in a network. In the first problem, we are given prescribed vertex subsets and the problem asks for finding the best location of roots of arc-disjoint arborescences that span these vertex subsets. We show that this problem is NP-hard in general and that it can be solved in polynomial time in the case where the prescribed vertex subsets are convex. In the second problem, we are given a demand d(v) for each vertex v and the problem asks for finding the best location of roots of arc-disjoint arborescences such that each vertex v is contained in at least d(v) arborescences. We show that this problem is NP-hard in general.

Original language | English |
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Pages (from-to) | 1964-1970 |

Number of pages | 7 |

Journal | Discrete Applied Mathematics |

Volume | 160 |

Issue number | 13-14 |

DOIs | |

Publication status | Published - Sep 1 2012 |

### All Science Journal Classification (ASJC) codes

- Discrete Mathematics and Combinatorics
- Applied Mathematics

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## Cite this

*Discrete Applied Mathematics*,

*160*(13-14), 1964-1970. https://doi.org/10.1016/j.dam.2012.04.013