Paper by Martin L. 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, volume 28, 2020, pages 942–958.

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 and from J-STAGE.

Length:

The paper is 19 pages.

Availability:

The paper is available in PDF (1403k).

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Tetris Font