On the Full and Bottleneck Full Steiner Tree Problems

Given a graph G = (V, E) with a length function on edges and a subset R of V , the full Steiner tree is defined to be a Steiner tree in G with all the vertices of R as its leaves. Then the full Steiner tree problem is to find a full Steiner tree in G with minimum length, and the bottleneck full Steiner tree problem is to find a full Steiner tree T in G such that the length of the largest edge in T is minimized. In this paper, we present a new approximation algorithm with performance ratio 2ρ for the full Steiner tree problem, where ρ is the best-known performance ratio for the Steiner tree problem. Moreover, we give an exact algorithm of O(|E| log |E|) time to solve the bottleneck full Steiner tree problem.