Tetris is NP-hard even with $O(1)$ rows or columns
Computational Complexity
2020-10-01 v1
Abstract
We prove that the classic falling-block video game Tetris (both survival and board clearing) remains NP-complete even when restricted to 8 columns, or to 4 rows, settling open problems posed over 15 years ago [BDH+04]. Our reduction is from 3-Partition, similar to the previous reduction for unrestricted board sizes, but with a better packing of buckets. On the positive side, we prove that 2-column Tetris (and 1-row Tetris) is polynomial. We also prove that the generalization of Tetris to larger -omino pieces is NP-complete even when the board starts empty, even when restricted to 3 columns or 2 rows or constant-size pieces. Finally, we present an animated Tetris font.
Cite
@article{arxiv.2009.14336,
title = {Tetris is NP-hard even with $O(1)$ rows or columns},
author = {Sualeh Asif and Michael Coulombe and Erik D. Demaine and Martin L. Demaine and Adam Hesterberg and Jayson Lynch and Mihir Singhal},
journal= {arXiv preprint arXiv:2009.14336},
year = {2020}
}
Comments
25 pages, 29 figures