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.APPROX-RANDOM.2017.13
URN: urn:nbn:de:0030-drops-75620
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Jansen, Klaus ; Klein, Kim-Manuel ; Kosche, Maria ; Ladewig, Leon

Online Strip Packing with Polynomial Migration

LIPIcs-APPROX-RANDOM-2017-13.pdf (1.0 MB)


We consider the relaxed online strip packing problem, where rectangular items arrive online and have to be packed into a strip of fixed width such that the packing height is minimized. Thereby, repacking of previously packed items is allowed. The amount of repacking is measured by the migration factor, defined as the total size of repacked items divided by the size of the arriving item. First, we show that no algorithm with constant migration factor can produce solutions with asymptotic ratio better than 4/3. Against this background, we allow amortized migration, i.e. to save migration for a later time step. As a main result, we present an AFPTAS with asymptotic ratio 1 + O(epsilon) for any epsilon > 0 and amortized migration factor polynomial in 1/epsilon. To our best knowledge, this is the first algorithm for online strip packing considered in a repacking model.

BibTeX - Entry

  author =	{Klaus Jansen and Kim-Manuel Klein and Maria Kosche and Leon Ladewig},
  title =	{{Online Strip Packing with Polynomial Migration}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)},
  pages =	{13:1--13:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-044-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{81},
  editor =	{Klaus Jansen and Jos{\'e} D. P. Rolim and David Williamson and Santosh S. Vempala},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-75620},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2017.13},
  annote =	{Keywords: strip packing, bin packing, online algorithms, migration factor}

Keywords: strip packing, bin packing, online algorithms, migration factor
Collection: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)
Issue Date: 2017
Date of publication: 11.08.2017

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