A Better Constant-Factor Approximation for Selected-Internal Steiner Minimum Tree

The selected-internal Steiner minimum tree problem is a generalization of original Steiner minimum tree problem. Given a weighted complete graph G=(V,E) with weight function c, and two subsets R (') aSS RaS dagger V with |R-R (')|a parts per thousand yen2, selected-internal Steiner minimum tree problem is to find a minimum subtree T of G interconnecting R such that any leaf of T does not belong to R ('). In this paper, suppose c is metric, we obtain a (1+rho)-approximation algorithm for this problem, where rho is the best-known approximation ratio for the Steiner minimum tree problem.