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Modern Heuristic Search Methods for the Steiner Tree Problem in Graphs

  • Chapter
Advances in Steiner Trees

Part of the book series: Combinatorial Optimization ((COOP,volume 6))

Abstract

Given an edge-weighted graph, the Steiner tree problem in graphs is to determine a minimum cost subgraph spanning a set of specified vertices. More specifically, consider an undirected connected graph G = (V, E) with vertex set V, edge set E, and nonnegative weights associated with the edges. Given a set Q ⊆ V of basic vertices Steiner’s problem in graphs (SP) is to find a minimum cost subgraph of G such that there exists a path in the subgraph between every pair of basic (or required) vertices. In order to achieve this minimum cost subgraph additional vertices from the set S:= V— Q, socalled Steiner vertices, may be included. Since all edge weights are assumed to be nonnegative, there is an optimal solution which is a tree, a so-called Steiner tree.

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  1. Institut für Wirtschaftswissenschaften, Technische Universität Braunschweig, Abt-Jerusalem-Straße 7, D - 38106, Braunschweig, Germany

    Stefan Voß

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  1. Department of Computer Science, University of Minnesota, USA

    Ding-Zhu Du

  2. Department of Mechanical & Industrial Engineering, University of Massachusetts, USA

    J. M. Smith

  3. Department of Mathematics, University of Melbourne, Australia

    J. H. Rubinstein

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Voß, S. (2000). Modern Heuristic Search Methods for the Steiner Tree Problem in Graphs. In: Du, DZ., Smith, J.M., Rubinstein, J.H. (eds) Advances in Steiner Trees. Combinatorial Optimization, vol 6. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3171-2_13

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