Approximation Algorithms for Packing Element-Disjoint Steiner Trees on Bounded Terminal Nodes

In this paper we discuss approximation algorithms for the Element-Disjoint Steiner Tree Packing problem (Element-STP for short). For a graph G = (V, E) and a subset of nodes T subset of V, called terminal nodes, a Steiner tree is a connected, acyclic subgraph that contains all the terminal nodes in T. The goal of Element-STP is to find as many element-disjoint Steiner trees as possible. Element-STP is known to be APX-hard even for vertical bar T vertical bar = 3 [1]. It is also known that Element-STP is NP-hard to approximate within a factor of Omega(log vertical bar V vertical bar) [3] and there is an Omega(log vertical bar V vertical bar)-approximation algorithm for Element-STP [2,4]. In this paper, we provide a inverted right perpendicular vertical bar T vertical bar/2inverted left perpendicular-approximation algorithm for Element-STP on graphs with vertical bar T vertical bar terminal nodes. Furthermore, we show that the approximation ratio of 3 for Element-STP on graphs with five terminal nodes can be improved to 2.