On the exact complexity of polyomino packing

Hans L. Bodlaender, Tom C. van der Zanden*

*Corresponding author for this work

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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. (C) 2020 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)13-20
Number of pages8
JournalTheoretical Computer Science
Publication statusPublished - 2 Nov 2020


  • Polyomino packing
  • Exact complexity
  • Exponential time hypothesis


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