Packing 2D Disks into a 3D Container

  • Helmut AltEmail author
  • Otfried Cheong
  • Ji-won Park
  • Nadja Scharf
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11355)


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.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Helmut Alt
    • 1
    Email author
  • Otfried Cheong
    • 2
  • Ji-won Park
    • 2
  • Nadja Scharf
    • 1
  1. 1.Institut für InformatikFreie Universität BerlinBerlinGermany
  2. 2.School of ComputingKAISTDaejeonSouth Korea

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