Approximating shallow-light trees

This paper deals with the problem of constructing Steiner trees of minimum weight with diameter bounded by d, spanning a given set, V of ν vertices in a graph. Exact solutions or logarithmic ratio approximation algorithms were known before for the cases of d≤5. Here we give a polynomial time approximation algorithm of ratio d log ν for constant d, and an algorithm of ratio ν^ε, for any fixed 0<ε<1, for general d.