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The three-dimensional matching problem in Kalmanson matrices

Author

Listed:
  • Sergey Polyakovskiy

    (Katholieke Universiteit Leuven)

  • Frits C. R. Spieksma

    (Katholieke Universiteit Leuven)

  • Gerhard J. Woeginger

    (TU Eindhoven)

Abstract

We investigate the computational complexity of several special cases of the three-dimensional matching problem where the costs are decomposable and determined by a so-called Kalmanson matrix. For the minimization version we develop an efficient polynomial time algorithm that is based on dynamic programming. For the maximization version, we show that there is a universally optimal matching (whose structure is independent of the particular Kalmanson matrix).

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:26:y:2013:i:1:d:10.1007_s10878-011-9426-y
    DOI: 10.1007/s10878-011-9426-y
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    References listed on IDEAS

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    1. Crama, Yves & Spieksma, Frits C. R., 1992. "Approximation algorithms for three-dimensional assignment problems with triangle inequalities," European Journal of Operational Research, Elsevier, vol. 60(3), pages 273-279, August.
    2. 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.
    3. Spieksma, Frits C. R. & Woeginger, Gerhard J., 1996. "Geometric three-dimensional assignment problems," European Journal of Operational Research, Elsevier, vol. 91(3), pages 611-618, June.
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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. 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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