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Steiner Tree 1.39-Approximation in Practice

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Book cover Mathematical and Engineering Methods in Computer Science (MEMICS 2014)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 8934))

Abstract

We consider the currently strongest Steiner tree approximation algorithm that has recently been published by Goemans, Olver, Rothvoß and Zenklusen (2012). It first solves a hypergraphic LP relaxation and then applies matroid theory to obtain an integral solution. The cost of the resulting Steiner tree is at most \((1.39 + \varepsilon )\)-times the cost of an optimal Steiner tree where \(\varepsilon \) tends to zero as some parameter \(k\) tends to infinity. However, the degree of the polynomial running time depends on this constant \(k\), so only small \(k\) are tractable in practice.

The algorithm has, to our knowledge, not been implemented and evaluated in practice before. We investigate different implementation aspects and parameter choices of the algorithm and compare tuned variants to an exact LP-based algorithm as well as to fast and simple \(2\)-approximations.

Funded by the German Research Foundation (DFG), project CH 897/1-1.

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Authors and Affiliations

  1. Institute of Computer Science, University of Osnabrück, Osnabrück, Germany

    Stephan Beyer & Markus Chimani

Authors
  1. Stephan Beyer
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  2. Markus Chimani
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Correspondence to Stephan Beyer .

Editor information

Editors and Affiliations

  1. Masaryk University, Brno, Czech Republic

    Petr Hliněný

  2. Charles University, Praha, Czech Republic

    Zdeněk Dvořák

  3. Brno University of Technology, Brno, Czech Republic

    Jiří Jaroš

  4. Charles University, Praha, Czech Republic

    Jan Kofroň

  5. Brno University of Technology, Brno, Czech Republic

    Jan Kořenek

  6. Masaryk University, Brno, Czech Republic

    Petr Matula

  7. Masaryk University, Brno, Czech Republic

    Karel Pala

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Beyer, S., Chimani, M. (2014). Steiner Tree 1.39-Approximation in Practice. In: Hliněný, P., et al. Mathematical and Engineering Methods in Computer Science. MEMICS 2014. Lecture Notes in Computer Science(), vol 8934. Springer, Cham. https://doi.org/10.1007/978-3-319-14896-0_6

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  • DOI: https://doi.org/10.1007/978-3-319-14896-0_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-14895-3

  • Online ISBN: 978-3-319-14896-0

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