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

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

## Abstract

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.

## Keywords

Approximation Algorithm Bipartite Graph Approximation Ratio Terminal Node Steiner Tree
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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