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Linearizable special cases of the QAP

Author

Listed:
  • Eranda Çela

    (TU Graz)

  • Vladimir G. Deineko

    (The University of Warwick)

  • Gerhard J. Woeginger

    (TU Eindhoven)

Abstract

We consider special cases of the quadratic assignment problem (QAP) that are linearizable in the sense of Bookhold. We provide combinatorial characterizations of the linearizable instances of the weighted feedback arc set QAP, and of the linearizable instances of the traveling salesman QAP. As a by-product, this yields a new well-solvable special case of the weighted feedback arc set problem.

Suggested Citation

  • Eranda Çela & Vladimir G. Deineko & Gerhard J. Woeginger, 2016. "Linearizable special cases of the QAP," Journal of Combinatorial Optimization, Springer, vol. 31(3), pages 1269-1279, April.
    • Handle: RePEc:spr:jcomop:v:31:y:2016:i:3:d:10.1007_s10878-014-9821-2
    DOI: 10.1007/s10878-014-9821-2
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    References listed on IDEAS

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    1. Santosh N. Kabadi & Abraham P. Punnen, 2011. "An O ( n 4 ) Algorithm for the QAP Linearization Problem," Mathematics of Operations Research, INFORMS, vol. 36(4), pages 754-761, November.
    2. Berenguer, Xavier, 1979. "A characterization of linear admissible transformations for the m-travelling salesmen problem," European Journal of Operational Research, Elsevier, vol. 3(3), pages 232-238, May.
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    Cited by:

    1. de Meijer, Frank, 2023. "Integrality and cutting planes in semidefinite programming approaches for combinatorial optimization," Other publications TiSEM b1f1088c-95fe-4b8a-9e15-c, Tilburg University, School of Economics and Management.
    2. Hao Hu & Renata Sotirov, 2018. "Special cases of the quadratic shortest path problem," Journal of Combinatorial Optimization, Springer, vol. 35(3), pages 754-777, April.
    3. Ante Ćustić & Abraham P. Punnen, 2018. "A characterization of linearizable instances of the quadratic minimum spanning tree problem," Journal of Combinatorial Optimization, Springer, vol. 35(2), pages 436-453, February.
    4. Hao Hu & Renata Sotirov, 2021. "The linearization problem of a binary quadratic problem and its applications," Annals of Operations Research, Springer, vol. 307(1), pages 229-249, December.

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