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Polyhedral Approaches for the Steiner Tree Problem on Graphs

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Steiner Trees in Industry

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

Abstract

Given an undirected graph G = (V, E) and a node set \(T \subseteq V\), a Steiner tree for T in G is a set of edges \(S \subseteq E\) such that the graph (V(S), S) contains a path between every pair of nodes in T, where V(S) is the set of nodes incident to the edges in S. Given costs (or weights) on edges and nodes, the Steiner tree problem on a graph (STP) is to find a minimum weight Steiner tree. The problem is known to be \(\mathcal{N}\mathcal{P}\)-hard even for planar graphs, bipartite graphs, and grid graphs.

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Author information

Authors and Affiliations

  1. Kellogg Graduate School of Management, Northwestern University, Evanston, IL, 60208, USA

    Sunil Chopra

  2. School of Business Administration, The State University of New York at New Paltz, New Paltz, NY, 12561, USA

    Chih-Yang Tsai

Authors
  1. Sunil Chopra
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  2. Chih-Yang Tsai
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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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Chopra, S., Tsai, CY. (2001). Polyhedral Approaches for the Steiner Tree Problem on 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_5

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  • DOI: https://doi.org/10.1007/978-1-4613-0255-1_5

  • 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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