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The quadratic minimum spanning tree problem

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  • Arjang Assad
  • Weixuan Xu

Abstract

This article introduces a new optimization problem that involves searching for the spanning tree of minimum cost under a quadratic cost structure. This quadratic minimum spanning tree problem is proven to be NP‐hard. A technique for generating lower bounds for this problem is discussed and incorporated into branch‐and‐bound schemes for obtaining exact solutions. Two heuristic algorithms are also developed. Computational experience with both exact and heuristic algorithms is reported.

Suggested Citation

  • Arjang Assad & Weixuan Xu, 1992. "The quadratic minimum spanning tree problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(3), pages 399-417, April.
    • Handle: RePEc:wly:navres:v:39:y:1992:i:3:p:399-417
    DOI: 10.1002/1520-6750(199204)39:33.0.CO;2-0
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    References listed on IDEAS

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    1. Kusiak, Andrew & Heragu, Sunderesh S., 1987. "The facility layout problem," European Journal of Operational Research, Elsevier, vol. 29(3), pages 229-251, June.
    2. A. Charnes & W. W. Cooper, 1963. "Deterministic Equivalents for Optimizing and Satisficing under Chance Constraints," Operations Research, INFORMS, vol. 11(1), pages 18-39, February.
    3. Robin Segerblom Liggett, 1981. "The Quadratic Assignment Problem: An Experimental Evaluation of Solution Strategies," Management Science, INFORMS, vol. 27(4), pages 442-458, April.
    4. Burkard, Rainer E., 1984. "Quadratic assignment problems," European Journal of Operational Research, Elsevier, vol. 15(3), pages 283-289, March.
    5. Kaku, Bharat K & Thompson, Gerald L., 1986. "An exact algorithm for the general quadratic assignment problem," European Journal of Operational Research, Elsevier, vol. 23(3), pages 382-390, March.
    6. Connolly, David T., 1990. "An improved annealing scheme for the QAP," European Journal of Operational Research, Elsevier, vol. 46(1), pages 93-100, May.
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    Cited by:

    1. Christoph Buchheim & Emiliano Traversi, 2018. "Quadratic Combinatorial Optimization Using Separable Underestimators," INFORMS Journal on Computing, INFORMS, vol. 30(3), pages 424-437, August.
    2. 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.
    3. Abraham P. Punnen & Ruonan Zhang, 2011. "Quadratic bottleneck problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(2), pages 153-164, March.
    4. 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.
    5. Pereira, Dilson Lucas & Salles da Cunha, Alexandre, 2020. "Dynamic intersection of multiple implicit Dantzig–Wolfe decompositions applied to the adjacent only quadratic minimum spanning tree problem," European Journal of Operational Research, Elsevier, vol. 284(2), pages 413-426.

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