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Generalized Hanan Grids for Geometric Steiner Trees in Uniform Orientation Metrics

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Abstract

Given a finite set of points in some metric space, a fundamental task is to find a shortest network interconnecting all of them. The network may include additional points, so-called Steiner points, which can be inserted at arbitrary places in order to minimize the total length with respect to the given metric. This paper focuses on uniform orientation metrics where the edges of the network are restricted to lie within a given set of legal directions. We here review the crucial insight that many versions of geometric network design problems can be reduced to the Steiner tree problem in finite graphs, namely the Hanan grid or its extensions.

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Authors and Affiliations

  1. Institut für Informatik, Martin-Luther-Universität Halle-Wittenberg, Von-Seckendorff-Platz 1, 06120, Halle (Saale), Germany

    Matthias Müller-Hannemann

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  1. Matthias Müller-Hannemann
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Correspondence to Matthias Müller-Hannemann .

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Editors and Affiliations

  1. Technische Universität München, Munich, Germany

    Andreas S. Schulz

  2. Institute of Mathematics, Technische Universität Berlin, Berlin, Berlin, Germany

    Martin Skutella

  3. Technische Universität Braunschweig, Braunschweig, Germany

    Sebastian Stiller

  4. Institute of Theoretical Informatics, Karlsruher Institut für Technologie (KIT), Karlsruhe, Germany

    Dorothea Wagner

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Müller-Hannemann, M. (2015). Generalized Hanan Grids for Geometric Steiner Trees in Uniform Orientation Metrics. In: Schulz, A., Skutella, M., Stiller, S., Wagner, D. (eds) Gems of Combinatorial Optimization and Graph Algorithms . Springer, Cham. https://doi.org/10.1007/978-3-319-24971-1_4

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