TY - JOUR
T1 - The root location problem for arc-disjoint arborescences
AU - Fujishige, Satoru
AU - Kamiyama, Naoyuki
N1 - Funding Information:
The authors are partly supported by a Grants in Aid for Scientific Research from Japan Society for the Promotion of Science .
PY - 2012/9
Y1 - 2012/9
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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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 -