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Steiner Tree Heuristic in the Euclidean d-Space Using Bottleneck Distances

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Experimental Algorithms (SEA 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9685))

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Abstract

Some of the most efficient heuristics for the Euclidean Steiner minimal tree problem in the d-dimensional space, \(d \ge 2\), use Delaunay tessellations and minimum spanning trees to determine small subsets of geometrically close terminals. Their low-cost Steiner trees are determined and concatenated in a greedy fashion to obtain a low cost tree spanning all terminals. The weakness of this approach is that obtained solutions are topologically related to minimum spanning trees. To avoid this and to obtain even better solutions, bottleneck distances are utilized to determine good subsets of terminals without being constrained by the topologies of minimum spanning trees. Computational experiments show a significant solution quality improvement.

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Authors and Affiliations

  1. Department of Computer Science, University of Copenhagen, Universitetsparken 5, 2100, Copenhagen O, Denmark

    Stephan S. Lorenzen & Pawel Winter

Authors
  1. Stephan S. Lorenzen
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  2. Pawel Winter
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Correspondence to Pawel Winter .

Editor information

Editors and Affiliations

  1. Amazon.com, Inc., Palo Alto, California, USA

    Andrew V. Goldberg

  2. Russian Academy of Sciences, St. Petersburg, Russia

    Alexander S. Kulikov

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Lorenzen, S.S., Winter, P. (2016). Steiner Tree Heuristic in the Euclidean d-Space Using Bottleneck Distances. In: Goldberg, A., Kulikov, A. (eds) Experimental Algorithms. SEA 2016. Lecture Notes in Computer Science(), vol 9685. Springer, Cham. https://doi.org/10.1007/978-3-319-38851-9_15

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  • DOI: https://doi.org/10.1007/978-3-319-38851-9_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-38850-2

  • Online ISBN: 978-3-319-38851-9

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