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

SN - 0166-218X

VL - 160

SP - 1964

EP - 1970

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

IS - 13-14

ER -