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

Yiping Lu (), Danny Z. Chen () and Jianzhong Cha ()
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Yiping Lu: Beijing Jiaotong University
Danny Z. Chen: University of Notre Dame
Jianzhong Cha: Beijing Jiaotong University

Journal of Combinatorial Optimization, 2015, vol. 29, issue 1, No 12, 197-215

Abstract: 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.

Keywords: Computational complexity; Packing problems; Cube packing; Bin packing; NP-completeness (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10878-013-9701-1

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