# The root location problem for arc-disjoint arborescences

Satoru Fujishige, Naoyuki Kamiyama

Research output: Contribution to journalArticle

1 Citation (Scopus)

### 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 1964-1970 7 Discrete Applied Mathematics 160 13-14 https://doi.org/10.1016/j.dam.2012.04.013 Published - Sep 1 2012

### Fingerprint

Location Problem
Disjoint
Arc of a curve
Roots
Vertex of a graph
Computational complexity
Subset
NP-complete problem
Polynomials
Polynomial time

### All Science Journal Classification (ASJC) codes

• Applied Mathematics
• Discrete Mathematics and Combinatorics

### Cite this

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

In: Discrete Applied Mathematics, Vol. 160, No. 13-14, 01.09.2012, p. 1964-1970.

Research output: Contribution to journalArticle

Fujishige, Satoru ; Kamiyama, Naoyuki. / The root location problem for arc-disjoint arborescences. In: Discrete Applied Mathematics. 2012 ; Vol. 160, No. 13-14. pp. 1964-1970.
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