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

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 ≥ 3 ) problems of packing hypercubes into a hypercube remains an open question (Acta Inf...

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Veröffentlicht in:	Journal of combinatorial optimization 2015-01, Vol.29 (1), p.197-215
Hauptverfasser:	Lu, Yiping, Chen, Danny Z., Cha, Jianzhong
Format:	Artikel
Sprache:	eng
Schlagworte:	Combinatorics Convex and Discrete Geometry Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Operations Research/Decision Theory Optimization Theory of Computation
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Zusammenfassung:	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 ≥ 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.
ISSN:	1382-6905 1573-2886
DOI:	10.1007/s10878-013-9701-1