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MAX-SNP Hardness and Approximation of Selected-Internal Steiner Trees

  • Sun-Yuan Hsieh
  • Shih-Cheng Yang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4112)

Abstract

In this paper, we consider an interesting variant of the well-known Steiner tree problem: Given a complete graph G = (V,E) with a cost function c:ER  +  and two subsets R and R′ satisfying R′ ⊂ R ⊆ V, a selected-internal Steiner tree is a Steiner tree which contains (or spans) all the vertices in R such that each vertex in R′ cannot be a leaf. The selected-internal Steiner tree problem is to find a selected-internal Steiner tree with the minimum cost. In this paper, we show that the problem is MAX SNP-hard even when the costs of all edges in the input graph are restricted to either 1 or 2. We also present an approximation algorithm for the problem.

Keywords

Cost Function Approximation Algorithm Complete Graph Steiner Tree Internal Vertex 
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 2006

Authors and Affiliations

  • Sun-Yuan Hsieh
    • 1
  • Shih-Cheng Yang
    • 1
  1. 1.Department of Computer Science and Information EngineeringNational Cheng Kung UniversityTainanTaiwan

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