Tetris is NP-hard even with O (1) Rows or Columns
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paper (1).pdf
Description
Accepted version
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1.37 MB
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Author(s)
Asif, Sualeh
Coulombe, Michael
Demaine, Erik D
Demaine, Martin L
Hesterberg, Adam
Lynch, Jayson
Singhal, Mihir
Date Issued
2020
Journal
Journal of Information Processing
Publisher
Information Processing Society of Japan
Citation
Asif, Sualeh, Coulombe, Michael, Demaine, Erik D, Demaine, Martin L, Hesterberg, Adam et al. 2020. "Tetris is NP-hard even with O (1) Rows or Columns." Journal of Information Processing, 28 (0).
Version
Author's final manuscript
Abstract
© 2020 Information Processing Society of Japan. 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.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.2197/IPSJJIP.28.942
