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
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 journal › Article
}
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.
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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 -