Packing Trominoes is NP-Complete, #P-Complete and ASP-Complete
Takashi Horiyama, Takehiro Ito, Keita Nakatsuka, Akira Suzuki, Ryuhei Uehara · 2013
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. 1