Approximating the selected-internal Steiner tree

In this paper, we consider a variant of the well-known Steiner tree problem. Given a complete graph G=(V,E) with a cost function c:E->R^+ and two subsets R and R^' satisfying R^'@[email protected]?V, a selected-internal Steiner tree is a Steiner tree which contains (or spans) all the vertices in R such that each vertex in R^' cannot be a leaf. The selected-internal Steiner tree problem is to find a selected-internal Steiner tree with the minimum cost. In this paper, we present a [email protected] algorithm for the problem, where @r is the best-known approximation ratio for the Steiner tree problem.