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.2016.11
URN: urn:nbn:de:0030-drops-67801
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6780/
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Alt, Helmut ; Scharf, Nadja

Approximating Smallest Containers for Packing Three-Dimensional Convex Objects

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LIPIcs-ISAAC-2016-11.pdf (0.6 MB)

Abstract

We investigate the problem of computing a minimum-volume container for the non-overlapping packing of a given set of three-dimensional convex objects. Already the simplest versions of the problem are NP-hard so that we cannot expect to find exact polynomial time algorithms.

We give constant ratio approximation algorithms for packing axis-parallel (rectangular) cuboids under translation into an axis-parallel (rectangular) cuboid as container, for packing cuboids under rigid motions into an axis-parallel cuboid or into an arbitrary convex container, and for packing convex polyhedra under rigid motions into an axis-parallel cuboid or arbitrary convex container. This work gives the first approximability results for the computation of minimum volume containers for the objects described.

BibTeX - Entry

@InProceedings{alt_et_al:LIPIcs:2016:6780,
  author =	{Helmut Alt and Nadja Scharf},
  title =	{{Approximating Smallest Containers for Packing Three-Dimensional Convex Objects}},
  booktitle =	{27th International Symposium on Algorithms and Computation (ISAAC 2016)},
  pages =	{11:1--11:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-026-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{64},
  editor =	{Seok-Hee Hong},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6780},
  URN =		{urn:nbn:de:0030-drops-67801},
  doi =		{10.4230/LIPIcs.ISAAC.2016.11},
  annote =	{Keywords: computational geometry, packing, approximation algorithm}
}

Keywords: computational geometry, packing, approximation algorithm
Collection: 27th International Symposium on Algorithms and Computation (ISAAC 2016)
Issue Date: 2016
Date of publication: 07.12.2016

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