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1.25-Approximation Algorithm for Steiner Tree Problem with Distances 1 and 2

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Algorithms and Data Structures (WADS 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5664))

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Abstract

Given a connected graph G = (V,E) with nonnegative costs on edges, \(c:E\rightarrow {\mathcal R}^+\), and a subset of terminal nodes R ⊂ V, the Steiner tree problem asks for the minimum cost subgraph of G spanning R. The Steiner Tree Problem with distances 1 and 2 (i.e., when the cost of any edge is either 1 or 2) has been investigated for long time since it is MAX SNP-hard and admits better approximations than the general problem. We give a 1.25 approximation algorithm for the Steiner Tree Problem with distances 1 and 2, improving on the previously best known ratio of 1.279.

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References

  1. Bern, M., Plassmann, P.: The Steiner problem with edge lengths 1 and 2. Information Processing letters 32, 171–176 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  2. Rayward-Smith, V.J.: The computation of nearly minimal Steiner trees in graphs. Internat. J. Math. Educ. Sci. Tech. 14, 15–23 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  3. Robins, G., Zelikovsky, A.: Tighter Bounds for Graph Steiner Tree Approximation. SIAM Journal on Discrete Mathematics 19(1), 122–134 (2005); Preliminary version appeared in Proc. SODA 2000, pp. 770–779

    Article  MathSciNet  MATH  Google Scholar 

  4. Gabow, H.N., Stallmann, M.: An augmenting path algorithm for linear matroid parity. Combinatorica 6, 123–150 (1986)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science & Engineering, Pennsylvania State University, University Park, PA, 16802, USA

    Piotr Berman

  2. Department of Computer Science, University of Bonn, 53117, Bonn, Germany

    Marek Karpinski

  3. Department of Computer Science, Georgia State University, Atlanta, GA, 30303, USA

    Alexander Zelikovsky

Authors
  1. Piotr Berman
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  2. Marek Karpinski
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  3. Alexander Zelikovsky
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Editor information

Editors and Affiliations

  1. Carleton University, Ottawa, Canada

    Frank Dehne

  2. Department of Computer Science, University of Calgary, 2500 University Drive N.W., T2N 1N4, Calgary, AB, Canada

    Marina Gavrilova

  3. School of Computer Science, Carleton University, 1125 Colonel By Drive, Ottawa, P.O. Box, K1S 5B6, Ontario, Canada

    Jörg-Rüdiger Sack

  4. University of Calgary, Calgary, AB, Canada

    Csaba D. Tóth

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© 2009 Springer-Verlag Berlin Heidelberg

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Berman, P., Karpinski, M., Zelikovsky, A. (2009). 1.25-Approximation Algorithm for Steiner Tree Problem with Distances 1 and 2. In: Dehne, F., Gavrilova, M., Sack, JR., Tóth , C.D. (eds) Algorithms and Data Structures. WADS 2009. Lecture Notes in Computer Science, vol 5664. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03367-4_8

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  • DOI: https://doi.org/10.1007/978-3-642-03367-4_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03366-7

  • Online ISBN: 978-3-642-03367-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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