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

摘要

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.