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Approximation Algorithms for the Steiner Tree Problem in Graphs

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Steiner Trees in Industry

Part of the book series: Combinatorial Optimization ((COOP,volume 11))

Abstract

Given a graph G = (V, E), a set R \(R \subseteq V\) V, and a length function on the edges, a Steiner tree is a connected subgraph of G that spans all vertices in R. (It might use vertices in V \ R as well.) The Steiner tree problem in graphs is to find a shortest Steiner tree, i.e., a Steiner tree whose total edge length is minimum. This problem is well known to be NP-hard [19] and therefore we cannot expect to find polynomial time algorithms for solving it exactly. This motivates the search for good approximation algorithms for the Steiner tree problem in graphs, i. e., algorithms that have polynomial running time and return solutions that are not far from an optimum solution.

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Author information

Authors and Affiliations

  1. Institut für Informatik, Humboldt- Universität zu Berlin, 10099, Berlin, Germany

    Clemens Gröpl, Stefan Hougardy, Till Nierhoff & Hans Jürgen Prömel

Authors
  1. Clemens Gröpl
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  2. Stefan Hougardy
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  3. Till Nierhoff
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  4. Hans Jürgen Prömel
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, University of Minnesota, Minneapolis, MN, USA

    Xiu Zhen Cheng  & Ding-Zhu Du  & 

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© 2001 Kluwer Academic Publishers

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Gröpl, C., Hougardy, S., Nierhoff, T., Prömel, H.J. (2001). Approximation Algorithms for the Steiner Tree Problem in Graphs. In: Cheng, X.Z., Du, DZ. (eds) Steiner Trees in Industry. Combinatorial Optimization, vol 11. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0255-1_7

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  • DOI: https://doi.org/10.1007/978-1-4613-0255-1_7

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-7963-8

  • Online ISBN: 978-1-4613-0255-1

  • eBook Packages: Springer Book Archive

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