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Packing 2D Disks into a 3D Container

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WALCOM: Algorithms and Computation (WALCOM 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11355))

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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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References

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Author information

Authors and Affiliations

  1. Institut für Informatik, Freie Universität Berlin, Berlin, Germany

    Helmut Alt & Nadja Scharf

  2. School of Computing, KAIST, Daejeon, South Korea

    Otfried Cheong & Ji-won Park

Authors
  1. Helmut Alt
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  2. Otfried Cheong
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  3. Ji-won Park
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  4. Nadja Scharf
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Corresponding author

Correspondence to Helmut Alt .

Editor information

Editors and Affiliations

  1. Indian Institute of Technology Guwahati, Guwahati, India

    Gautam K. Das

  2. Indian Institute of Technology Guwahati, Guwahati, India

    Partha S. Mandal

  3. Indian Statistical Institute, Kolkata, India

    Krishnendu Mukhopadhyaya

  4. Gunma University, Kiryu, Japan

    Shin-ichi Nakano

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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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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-10563-1

  • Online ISBN: 978-3-030-10564-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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