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.2019.35
URN: urn:nbn:de:0030-drops-104398
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10439/
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Fekete, Sándor P. ; Keldenich, Phillip ; Scheffer, Christian

Packing Disks into Disks with Optimal Worst-Case Density

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LIPIcs-SoCG-2019-35.pdf (1.0 MB)

Abstract

We provide a tight result for a fundamental problem arising from packing disks into a circular container: The critical density of packing disks in a disk is 0.5. This implies that any set of (not necessarily equal) disks of total area delta <= 1/2 can always be packed into a disk of area 1; on the other hand, for any epsilon>0 there are sets of disks of area 1/2+epsilon that cannot be packed. The proof uses a careful manual analysis, complemented by a minor automatic part that is based on interval arithmetic. Beyond the basic mathematical importance, our result is also useful as a blackbox lemma for the analysis of recursive packing algorithms.

BibTeX - Entry

@InProceedings{fekete_et_al:LIPIcs:2019:10439,
  author =	{S{\'a}ndor P. Fekete and Phillip Keldenich and Christian Scheffer},
  title =	{{Packing Disks into Disks with Optimal Worst-Case Density}},
  booktitle =	{35th International Symposium on Computational Geometry (SoCG 2019)},
  pages =	{35:1--35:19},
  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 =		{http://drops.dagstuhl.de/opus/volltexte/2019/10439},
  URN =		{urn:nbn:de:0030-drops-104398},
  doi =		{10.4230/LIPIcs.SoCG.2019.35},
  annote =	{Keywords: Disk packing, packing density, tight worst-case bound, interval arithmetic, approximation}
}

Keywords: Disk packing, packing density, tight worst-case bound, interval arithmetic, approximation
Collection: 35th International Symposium on Computational Geometry (SoCG 2019)
Issue Date: 2019
Date of publication: 11.06.2019
Supplementary Material: https://github.com/phillip-keldenich/circlepacking

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