On the Internal Steiner Tree Problem

  • Sun-Yuan Hsieh
  • Huang-Ming Gao
  • Shih-Cheng Yang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4484)


Given a complete graph G = (V,E)with a cost function c : E →ℝ +  and a vertex subset R ⊂ V, an internal Steiner tree is a Steiner tree which contains all vertices in R such that each vertex in R is restricted to be an internal vertex. The internal Steiner tree problem is to find an internal Steiner tree T whose total costs ∑ (u,v) ∈ E(T) c(u,v) is minimum. In this paper, we first show that the internal Steiner tree problem is MAX SNP-hard. We then present an approximation algorithm with approximation ratio 2ρ + 1 for the problem, where ρ is the best known approximation ratio for the Steiner tree problem.


Approximation Algorithm Approximation Ratio Steiner Tree Internal Vertex Steiner Tree Problem 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Sun-Yuan Hsieh
    • 1
  • Huang-Ming Gao
    • 1
  • Shih-Cheng Yang
    • 1
  1. 1.Department of Computer Science and Information Engineering, National Cheng Kung University, No.1, University Road, Tainan 70101Taiwan

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