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Packing cubes into a cube is NP-complete in the strong sense

Author

Listed:
  • Yiping Lu

    (Beijing Jiaotong University)

  • Danny Z. Chen

    (University of Notre Dame)

  • Jianzhong Cha

    (Beijing Jiaotong University)

Abstract

While the problem of packing two-dimensional squares into a square, in which a set of squares is packed into a big square, has been proved to be NP-complete, the computational complexity of the d-dimensional ( $$ d\ge 3 $$ d ≥ 3 ) problems of packing hypercubes into a hypercube remains an open question (Acta Inf 41(9):595–606, 2005; Theor Comput Sci 410(44):4504–4532, 2009). In this paper, the authors show that the three-dimensional problem version of packing cubes into a cube is NP-complete in the strong sense.

Suggested Citation

  • Yiping Lu & Danny Z. Chen & Jianzhong Cha, 2015. "Packing cubes into a cube is NP-complete in the strong sense," Journal of Combinatorial Optimization, Springer, vol. 29(1), pages 197-215, January.
    • Handle: RePEc:spr:jcomop:v:29:y:2015:i:1:d:10.1007_s10878-013-9701-1
    DOI: 10.1007/s10878-013-9701-1
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    References listed on IDEAS

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    1. Wascher, Gerhard & Hau[ss]ner, Heike & Schumann, Holger, 2007. "An improved typology of cutting and packing problems," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1109-1130, December.
    2. Alberto Caprara & Andrea Lodi & Michele Monaci, 2005. "Fast Approximation Schemes for Two-Stage, Two-Dimensional Bin Packing," Mathematics of Operations Research, INFORMS, vol. 30(1), pages 150-172, February.
    3. Nikhil Bansal & José R. Correa & Claire Kenyon & Maxim Sviridenko, 2006. "Bin Packing in Multiple Dimensions: Inapproximability Results and Approximation Schemes," Mathematics of Operations Research, INFORMS, vol. 31(1), pages 31-49, February.
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    Cited by:

    1. Tim Wylie & Michael A. Schuh & Rafal A. Angryk, 2016. "Enabling high-dimensional range queries using kNN indexing techniques: approaches and empirical results," Journal of Combinatorial Optimization, Springer, vol. 32(4), pages 1107-1132, November.

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