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 (dā>ā2) 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.
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References
Bansal, N., Correa, J.R., Kenyon, C., Sviridenko, M.: Bin Packing in Multiple Dimensions: Inapproximability Results and Approximation Schemes. Mathematics of Operations ResearchĀ 31(1), 31ā49 (2006)
Caprara, A., Lodi, A., Monaci, M.: Fast Approximation Schemes for Two-stage, Two-dimensional Bin Packing. Mathematics of Operations ResearchĀ 30, 136ā156 (2005)
Chung, F.R.K., Garey, M.R., Johnson, D.S.: On Packing Two-dimensional Bins. SIAM Journal on Algebraic and Discrete MethodsĀ 3, 66ā76 (1982)
Correa, J.R., Kenyon, C.: Approximation Schemes for Multidimensional Packing. In: Proc. 15th ACMāSIAM Symposium on Discrete Algorithms, pp. 179ā188 (2004)
Epstein, L., van Stee, R.: Online Square and Cube Packing. Acta InformaticaĀ 41(9), 595ā606 (2005)
Garey, M., Johnson, D.: Computer and Intractability ā A Guide to the Theory of NP-Completeness. Freeman, New York (1979)
Harren, R.: Approximation Algorithms for Orthogonal Packing Problems for Hypercubes. Theoretical Computer ScienceĀ 410(44), 4504ā4532 (2009)
Kohayakawa, Y., Miyazawa, F.K., Raghavan, P., Wakabayashi, Y.: Multidimensional Cube Packing. AlgorithmicaĀ 40, 173ā187 (2004)
Leung, J.Y.-T., Tam, W.T., Wong, C.S., Chin, F.Y.L.: Packing Squares into a Square. Journal of Parallel and Distributed ComputingĀ 10, 271ā275 (1990)
Li, K., Cheng, K.H.: Complexity of Resource Allocation and Job Scheduling Problems in Partitionable Mesh Connected Systems. In: Proc. of 1st Annual IEEE Symposium of Parallel and Distributed Processing, Silver Spring, MD, pp. 358ā365 (1989)
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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: Du, DZ., Zhang, G. (eds) Computing and Combinatorics. COCOON 2013. Lecture Notes in Computer Science, vol 7936. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38768-5_53
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DOI: https://doi.org/10.1007/978-3-642-38768-5_53
Publisher Name: Springer, Berlin, Heidelberg
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