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DOI: 10.4230/LIPIcs.FUN.2018.9
URN: urn:nbn:de:0030-drops-88001
URL: https://drops.dagstuhl.de/opus/volltexte/2018/8800/
Bodlaender, Hans L. ; van der Zanden, Tom C.
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: | 04.06.2018 |
