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.