The root location problem for arc-disjoint arborescences

Authors:
Satoru Fujishige;Naoyuki Kamiyama
Affiliations:
Research Institute for Mathematical Sciences, Kyoto University, Japan;Institute of Mathematics for Industry, Kyushu University, Japan
Venue:
Discrete Applied Mathematics
Year:
2012

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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.