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The multi-stripe travelling salesman problem

Author

Listed:
  • Eranda Çela

    (TU Graz)

  • Vladimir G. Deineko

    (The University of Warwick)

  • Gerhard J. Woeginger

    (Lehrstuhl für Informatik 1, RWTH Aachen)

Abstract

In the classical Travelling Salesman Problem (TSP), the objective function sums the costs for travelling from one city to the next city along the tour. In the q-stripe TSP with $$q\ge 1$$ q ≥ 1 , the objective function sums the costs for travelling from one city to each of the next q cities in the tour. The resulting q-stripe TSP generalizes the TSP and forms a special case of the quadratic assignment problem. We analyze the computational complexity of the q-stripe TSP for various classes of specially structured distance matrices. We derive NP-hardness results as well as polynomially solvable cases. One of our main results generalizes a well-known theorem of Kalmanson from the classical TSP to the q-stripe TSP.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:259:y:2017:i:1:d:10.1007_s10479-017-2513-4
    DOI: 10.1007/s10479-017-2513-4
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    References listed on IDEAS

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    1. A. Kononov & S. Sevastianov & I. Tchernykh, 1999. "When difference in machine loads leadsto efficient scheduling in open shops," Annals of Operations Research, Springer, vol. 92(0), pages 211-239, January.
    2. E. Balas, 1999. "New classes of efficiently solvable generalized Traveling Salesman Problems," Annals of Operations Research, Springer, vol. 86(0), pages 529-558, January.
    3. 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.
    4. 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.
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