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

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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 > 2) problems of packing hypercubes into a hypercube remains an open question [5,7]. In this paper, we show that the three-dimensional problem version of packing cubes into a cube is NP-hard in the strong sense. © 2013 Springer-Verlag Berlin Heidelberg.

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Lu, Y., Chen, D. Z., & Cha, J. (2013). Packing cubes into a cube is NP-hard in the strong sense. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7936 LNCS, pp. 603–613). https://doi.org/10.1007/978-3-642-38768-5_53

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