Paper by Erik D. Demaine

Reference:
Sualeh Asif, Michael Coulombe, Erik D. Demaine, Martin L. Demaine, Adam Hesterberg, Jayson Lynch, and Mihir Singhal, “Tetris is NP-hard even with O(1) rows or columns”, Journal of Information Processing, to appear.

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 [2]. 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 k-omino pieces is NP-complete even when the board starts empty, and even when restricted to 3 columns or 2 rows or constant-size pieces. Finally, we present an animated Tetris font.

Comments:
This paper is available as arXiv:2009.14336.

Length:
The paper is 19 pages.

Availability:
The paper is available in PDF (1403k).
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Related papers:
ThinTetris_JCDCGGG2019 (Tetris is NP-hard even with O(1) Columns)


See also other papers by Erik Demaine.
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Last updated November 24, 2020 by Erik Demaine.