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.ISAAC.2017.4
URN: urn:nbn:de:0030-drops-82145
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Alt, Helmut ; Buchin, Kevin ; Chaplick, Steven ; Cheong, Otfried ; Kindermann, Philipp ; Knauer, Christian ; Stehn, Fabian

Placing your Coins on a Shelf

LIPIcs-ISAAC-2017-4.pdf (0.7 MB)


We consider the problem of packing a family of disks 'on a shelf,'
that is, such that each disk touches the x-axis from above and such that no two disks overlap. We prove that the problem of minimizing the distance between the leftmost point and the rightmost point of any disk is NP-hard. On the positive side, we show how to approximate this problem within a factor of 4/3 in O(n log n) time, and provide an O(n log n)-time exact algorithm for a special case, in particular when the ratio between the largest and smallest radius is at most four.

BibTeX - Entry

  author =	{Helmut Alt and Kevin Buchin and Steven Chaplick and Otfried Cheong and Philipp Kindermann and Christian Knauer and Fabian Stehn},
  title =	{{Placing your Coins on a Shelf}},
  booktitle =	{28th International Symposium on Algorithms and Computation (ISAAC 2017)},
  pages =	{4:1--4:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-054-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{92},
  editor =	{Yoshio Okamoto and Takeshi Tokuyama},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-82145},
  doi =		{10.4230/LIPIcs.ISAAC.2017.4},
  annote =	{Keywords: packing problems, approximation algorithms, NP-hardness}

Keywords: packing problems, approximation algorithms, NP-hardness
Collection: 28th International Symposium on Algorithms and Computation (ISAAC 2017)
Issue Date: 2017
Date of publication: 07.12.2017

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