License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2019.63
URN: urn:nbn:de:0030-drops-104678
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Becker, Aaron T. ; Fekete, Sándor P. ; Keldenich, Phillip ; Morr, Sebastian ; Scheffer, Christian

Packing Geometric Objects with Optimal Worst-Case Density (Multimedia Exposition)

LIPIcs-SoCG-2019-63.pdf (1 MB)


We motivate and visualize problems and methods for packing a set of objects into a given container, in particular a set of {different-size} circles or squares into a square or circular container. Questions of this type have attracted a considerable amount of attention and are known to be notoriously hard. We focus on a particularly simple criterion for deciding whether a set can be packed: comparing the total area A of all objects to the area C of the container. The critical packing density delta^* is the largest value A/C for which any set of area A can be packed into a container of area C. We describe algorithms that establish the critical density of squares in a square (delta^*=0.5), of circles in a square (delta^*=0.5390 ...), regular octagons in a square (delta^*=0.5685 ...), and circles in a circle (delta^*=0.5).

BibTeX - Entry

  author =	{Aaron T. Becker and S{\'a}ndor P. Fekete and Phillip Keldenich and Sebastian Morr and Christian Scheffer},
  title =	{{Packing Geometric Objects with Optimal Worst-Case Density (Multimedia Exposition)}},
  booktitle =	{35th International Symposium on Computational Geometry (SoCG 2019)},
  pages =	{63:1--63:6},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-104-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{129},
  editor =	{Gill Barequet and Yusu Wang},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-104678},
  doi =		{10.4230/LIPIcs.SoCG.2019.63},
  annote =	{Keywords: Packing, complexity, bounds, packing density}

Keywords: Packing, complexity, bounds, packing density
Collection: 35th International Symposium on Computational Geometry (SoCG 2019)
Issue Date: 2019
Date of publication: 11.06.2019

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