Abstract
In this article, we consider the problem of finding in three dimensions a minimum volume axis-parallel box into which a given set of unit size disks can be packed under translations. The problem is neither known to be NP-hard nor to be in NP. We give a constant factor approximation algorithm based on reduction to finding a shortest Hamiltonian path in a weighted graph. As a byproduct, we can show that there is no finite size container into which all unit disks can be packed simultaneously.
N. Scharf was partially supported by a fellowship within the FITweltweit program and H. Alt by the Johann-Gottfried-Herder program, both of the German Academic Exchange Service (DAAD). J. Park was supported in part by starlab project (IITP-2015-0-00199) and NRF-2017M3C4A7066317.
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Alt, H., Cheong, O., Park, Jw., Scharf, N. (2019). Packing 2D Disks into a 3D Container. In: Das, G., Mandal, P., Mukhopadhyaya, K., Nakano, Si. (eds) WALCOM: Algorithms and Computation. WALCOM 2019. Lecture Notes in Computer Science(), vol 11355. Springer, Cham. https://doi.org/10.1007/978-3-030-10564-8_29
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DOI: https://doi.org/10.1007/978-3-030-10564-8_29
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