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The Steiner Tree Problem in Kalmanson Matrices and in Circulant Matrices

Author

Listed:
  • Bettina Klinz

    (Institut für Mathematik, TU Graz)

  • Gerhard J. Woeginger

    (Institut für Mathematik, TU Graz)

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.

Suggested Citation

  • Bettina Klinz & Gerhard J. Woeginger, 1999. "The Steiner Tree Problem in Kalmanson Matrices and in Circulant Matrices," Journal of Combinatorial Optimization, Springer, vol. 3(1), pages 51-58, July.
    • Handle: RePEc:spr:jcomop:v:3:y:1999:i:1:d:10.1023_a:1009881510868
    DOI: 10.1023/A:1009881510868
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    Citations

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    Cited by:

    1. Eranda Çela & Vladimir G. Deineko & Gerhard J. Woeginger, 2017. "The multi-stripe travelling salesman problem," Annals of Operations Research, Springer, vol. 259(1), pages 21-34, December.
    2. Sergey Polyakovskiy & Frits C. R. Spieksma & Gerhard J. Woeginger, 2013. "The three-dimensional matching problem in Kalmanson matrices," Journal of Combinatorial Optimization, Springer, vol. 26(1), pages 1-9, July.
    3. Çela, Eranda & Deineko, Vladimir & Woeginger, Gerhard J., 2018. "New special cases of the Quadratic Assignment Problem with diagonally structured coefficient matrices," European Journal of Operational Research, Elsevier, vol. 267(3), pages 818-834.

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