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Approaches to the Steiner Problem in Networks

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Algorithmics of Large and Complex Networks

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5515))

Abstract

The Steiner problem in networks is the problem of connecting a set of required vertices in a weighted graph at minimum cost. This is a classical \({\mathcal {NP}}\)-hard problem and a fundamental problem in network design with many practical applications.

We approach this problem by various means: Relaxations, which relax the feasibility constraints, to get close to an optimal solution; heuristics to find good, but not necessarily optimal solutions; and reductions to simplify problem instances without abandoning the optimal solution. We have integrated these components into an exact algorithm that has achieved outstanding results in practice.

In this article, we first provide a brief overview on the main algorithmic developments related to our work on this problem, citing our and others’ (already published) works. Then we focus on some central concepts, presenting detailed results on selected topics that offer special insight and potential for further improvement.

Supported by the DFG, project NetDesign, KR 1521/6 (part of the DFG-SPP 1126).

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Author information

Authors and Affiliations

  1. HaCon Ingenieurgesellschaft mbH, Hannover, Germany

    Tobias Polzin

  2. Theoretische Informatik, Universität Mannheim, Germany

    Siavash Vahdati-Daneshmand

Authors
  1. Tobias Polzin
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  2. Siavash Vahdati-Daneshmand
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Editor information

Editors and Affiliations

  1. Department of Computer & Information Science, University of Konstanz, 78457, Konstanz, Germany

    Jürgen Lerner

  2. Institute of Theoretical Informatics, Technical University of Karlsruhe, 76128, Karlsruhe, Germany

    Dorothea Wagner

  3. Department of Biological Physics, Eötvös Lorand University, Pazmany P. Stny 1A, 1117, Budapest, Hungary

    Katharina A. Zweig

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Polzin, T., Vahdati-Daneshmand, S. (2009). Approaches to the Steiner Problem in Networks. In: Lerner, J., Wagner, D., Zweig, K.A. (eds) Algorithmics of Large and Complex Networks. Lecture Notes in Computer Science, vol 5515. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02094-0_5

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  • DOI: https://doi.org/10.1007/978-3-642-02094-0_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02093-3

  • Online ISBN: 978-3-642-02094-0

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