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On the Complexity of the Steiner Problem

Author

Listed:
  • M. Brazil

    (The University of Melbourne)

  • D.A. Thomas

    (The University of Melbourne)

  • J.F. Weng

    (The University of Melbourne)

Abstract

Recently Rubinstein et al. gave a new proof of the NP-completeness of the discretized Steiner problem, that is, the problem of finding a shortest network connecting a given set of points in the plane where all vertices are integer points and a discretized metric is used. Their approach was to consider the complexity of the PALIMEST problem, the Steiner problem for sets of points lying on two parallel lines. In this paper, we give a new proof of this theorem, using simpler, more constructive arguments. We then extend the result to a more general class of networks known as APE-Steiner trees in which certain angles between edges or slopes of edges are specified beforehand.

Suggested Citation

  • M. Brazil & D.A. Thomas & J.F. Weng, 2000. "On the Complexity of the Steiner Problem," Journal of Combinatorial Optimization, Springer, vol. 4(2), pages 187-195, June.
    • Handle: RePEc:spr:jcomop:v:4:y:2000:i:2:d:10.1023_a:1009846620554
    DOI: 10.1023/A:1009846620554
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    Cited by:

    1. Prosenjit Bose & Anthony D’Angelo & Stephane Durocher, 2022. "On the restricted k-Steiner tree problem," Journal of Combinatorial Optimization, Springer, vol. 44(4), pages 2893-2918, November.
    2. Alexander Westcott & Marcus Brazil & Charl Ras, 2023. "Structural Properties of Minimum Multi-source Multi-Sink Steiner Networks in the Euclidean Plane," Journal of Optimization Theory and Applications, Springer, vol. 197(3), pages 1104-1139, June.

    More about this item

    Keywords

    Steiner tree; computational complexity;

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