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

  • Daiki Hoshika
  • Eiji Miyano
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8546)


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 ⊆ 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 \({\cal APX}\)-hard even for |T| = 3 [1]. It is also known that Element-STP is \({\cal NP}\)-hard to approximate within a factor of Ω(log|V|) [3] and there is an O(log|V|)-approximation algorithm for Element-STP [2,4]. In this paper, we provide a \(\lceil \frac{|T|}{2}\rceil\)-approximation algorithm for Element-STP on graphs with |T| 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.


Approximation Algorithm Bipartite Graph Approximation Ratio Terminal Node Steiner Tree 
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© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Daiki Hoshika
    • 1
  • Eiji Miyano
    • 1
  1. 1.Department of Systems Design and InformaticsKyushu Institute of TechnologyIizukaJapan

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