Journal of Information Processing
Online ISSN : 1882-6652
ISSN-L : 1882-6652
Tetris is NP-hard even with O(1) Rows or Columns
Sualeh AsifMichael CoulombeErik D. DemaineMartin L. DemaineAdam HesterbergJayson LynchMihir Singhal
著者情報
キーワード: complexity, hardness, video games, font
ジャーナル フリー

2020 年 28 巻 p. 942-958

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抄録

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. 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.

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© 2020 by the Information Processing Society of Japan
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