Packing trominoes is np-complete, #p-complete and asp-complete

Takashi Horiyama, Takehiro Ito, Keita Nakatsuka, Akira Suzuki, Ryuhei Uehara

Research output: Contribution to conferencePaperpeer-review

3 Citations (Scopus)


We study the computational complexity of packing puzzles of identical polyominoes. Packing dominoes (i.e., 1 × 2 rectangles) into grid polygons can be solved in polynomial time by reducing to a bipartite matching problem. On the other hand, packing 2 × 2 squares is known to be NP-complete. In this paper, we fill the gap between dominoes and 2 × 2 squares, that is, we consider the packing puzzles of trominoes. Note that there exist only two shapes of trominoes: L-shape and I-shape. We show that their packing problems are both NP-complete. Our reductions are carefully designed so that we can also prove #P-completeness and ASPcompleteness of the counting and the another- solutionproblem variants, respectively.

Original languageEnglish
Number of pages6
Publication statusPublished - 2012
Event24th Canadian Conference on Computational Geometry, CCCG 2012 - Charlottetown, PE, Canada
Duration: 2012 Aug 82012 Aug 10


Conference24th Canadian Conference on Computational Geometry, CCCG 2012
CityCharlottetown, PE


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