Approximating the weight of shallow Steiner trees Original Research Article

This paper deals with the problem of constructing Steiner trees of minimum weight with diameter bounded by d, spanning a given set 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 O(log ν) for constant d, which is asymptotically optimal unless P=NP, and an algorithm of ratio O(νε), for any fixed 0<ε<1, for general d.