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The Steiner Tree Problem in Kalmanson Matrices and in Circulant Matrices

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Abstract

We investigate the computational complexity of two special cases of the Steiner tree problem where the distance matrix is a Kalmanson matrix or a circulant matrix, respectively. For Kalmanson matrices we develop an efficient polynomial time algorithm that is based on dynamic programming. For circulant matrices we give an \(\mathcal{N}\mathcal{P}\)-hardness proof and thus establish computational intractability.

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Authors and Affiliations

  1. Institut für Mathematik, TU Graz, Steyrergasse 30, A-8010, Graz, Austria

    Bettina Klinz & Gerhard J. Woeginger

Authors
  1. Bettina Klinz
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  2. Gerhard J. Woeginger
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Klinz, B., Woeginger, G.J. The Steiner Tree Problem in Kalmanson Matrices and in Circulant Matrices. Journal of Combinatorial Optimization 3, 51–58 (1999). https://doi.org/10.1023/A:1009881510868

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