In this article we study the group Steiner network problem, which is defined in the following way. Given a graph G ؍ (V,E), a partition of its vertices into K groups and connectivity requirements between the different groups, the aim is to find simultaneously a set of representatives, one for each group, and a minimum cost connected subgraph that satisfies the connectivity requirements between the groups (representatives). This problem is a generalization of the Steiner network problem and the group Steiner tree problem, two known NP-complete problems. We present an approximation algorithm for a special case of the group Steiner network problem with an approximation ratio of min {2(1 ؉ 2x),2I}, where I is the cardinality of the largest group and x is a parameter that depends on the cost function.
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