Diameter-constrained steiner tree

Abstract

Given an edge-weighted undirected graph G=(V,E,c,w), where each edge e ∈ E has a cost c(e) and a weight w(e), a set S⊆V of terminals and a positive constant D 0, we seek a minimum cost Steiner tree where all terminals appear as leaves and its diameter is bounded by D 0. Note that the diameter of a tree represents the maximum weight of path connecting two different leaves in the tree. Such problem is called the minimum cost diameter-constrained Steiner tree problem. This problem is NP-hard even when the topology of Steiner tree is fixed. In present paper we focus on this restricted version and present a fully polynomial time approximation scheme (FPTAS) for computing a minimum cost diameter-constrained Steiner tree under a fixed topology. © 2010 Springer-Verlag.