- INSTANCE: Directed multigraph , set of terminals , root .
- SOLUTION: A set of directed Steiner trees for rooted at in with pairwise disjoint sets of Steiner nodes.
- OBJECTIVE: Maximize.
*Approx.:*Approximable within approximation ratio , where m denotes the number of edges[34].*Hardness:*NP- hard to approximate within [34].

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