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Steiner Forest

1995; Agrawal, Klein, Ravi

  • Reference work entry
Encyclopedia of Algorithms

  • 389 Accesses

Keywords and Synonyms

Requirement join; R-join, Requirement Join    

Problem Definition

The Steiner forest problem is a fundamental problem in network design. Informally, the goal is to establish connections between pairs of vertices in a given network at minimum cost. The problem generalizes the well-known Steiner tree problem. As an example, assume that a telecommunication company receives communication requests from their customers. Each customer asks for a connection between two vertices in a given network. The company's goal is to build a minimum cost network infrastructure such that all communication requests are satisfied.

Formal Definition and Notation

More formally, an instance \( { I = (G, c, R) } \) of the Steiner forest problem is given by an undirected graph \( { G = (V, E) } \) with vertex set V and edge set E, a non-negative cost function \( { c\colon E \rightarrow \mathbb{Q}^+ } \), and a set of vertex pairs \( R = \{(s_1, t_1), \ldots, (s_k, t_k) \} \subseteq V \times V \)...

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Recommended Reading

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Author information

Authors and Affiliations

  1. Institute for Mathematics and Computer Science, Technical University of Berlin, Berlin, Germany

    Guido Schäfer

Authors
  1. Guido Schäfer
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Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer ScienceMcCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL, 60208, USA

    Ming-Yang Kao Professor of Computer Science

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© 2008 Springer-Verlag

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Schäfer, G. (2008). Steiner Forest. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30162-4_402

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