Diameter-constrained steiner trees

Given an edge-weighted undirected graph G = (V, E, c, w), where each edge e E has a non-negative cost c(e) and a non-negative weight w(e), a set S V of terminals and a positive constant D₀, we seek a minimum cost Steiner tree in which all terminals appear as leaves and the tree diameter is bounded by D₀. Here the tree diameter is the maximum weight of the paths connecting two different leaves in the tree. Such a problem is called the minimum cost diameter-constrained Steiner tree problem. The problem is NP-hard even when the topology of the Steiner tree is fixed. In present paper we focus on this fixed topology restricted version and present a fully polynomial time approximation scheme for computing a minimum cost diameter-constrained Steiner tree.