### 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 |
---|---|

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 |

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### All Science Journal Classification (ASJC) codes

- Applied Mathematics
- Discrete Mathematics and Combinatorics

### Cite this

*Discrete Applied Mathematics*,

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

**The root location problem for arc-disjoint arborescences.** / Fujishige, Satoru; Kamiyama, Naoyuki.

Research output: Contribution to journal › Article

*Discrete Applied Mathematics*, vol. 160, no. 13-14, pp. 1964-1970. https://doi.org/10.1016/j.dam.2012.04.013

}

TY - JOUR

T1 - The root location problem for arc-disjoint arborescences

AU - Fujishige, Satoru

AU - Kamiyama, Naoyuki

PY - 2012/9/1

Y1 - 2012/9/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84862205574&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84862205574&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2012.04.013

DO - 10.1016/j.dam.2012.04.013

M3 - Article

AN - SCOPUS:84862205574

VL - 160

SP - 1964

EP - 1970

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

IS - 13-14

ER -