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URN: urn:nbn:de:0030-drops-88001
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On the Exact Complexity of Polyomino Packing

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Abstract

We show that the problem of deciding whether a collection of polyominoes, each fitting in a 2 x O(log n) rectangle, can be packed into a 3 x n box does not admit a 2^{o(n/log{n})}-time algorithm, unless the Exponential Time Hypothesis fails. We also give an algorithm that attains this lower bound, solving any instance of polyomino packing with total area n in 2^{O(n/log{n})} time. This establishes a tight bound on the complexity of Polyomino Packing, even in a very restricted case. In contrast, for a 2 x n box, we show that the problem can be solved in strongly subexponential time.

BibTeX - Entry

@InProceedings{bodlaender_et_al:LIPIcs:2018:8800,
  author =	{Hans L. Bodlaender and Tom C. van der Zanden},
  title =	{{On the Exact Complexity of Polyomino Packing}},
  booktitle =	{9th International Conference on Fun with Algorithms (FUN 2018)},
  pages =	{9:1--9:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-067-5},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{100},
  editor =	{Hiro Ito and Stefano Leonardi and Linda Pagli and Giuseppe Prencipe},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8800},
  URN =		{urn:nbn:de:0030-drops-88001},
  doi =		{10.4230/LIPIcs.FUN.2018.9},
  annote =	{Keywords: polyomino packing, exact complexity, exponential time hypothesis}
}

Keywords: polyomino packing, exact complexity, exponential time hypothesis
Seminar: 9th International Conference on Fun with Algorithms (FUN 2018)
Issue date: 2018
Date of publication: 2018


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