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Tetris with Few Piece Types

Authors MIT Hardness Group, Erik D. Demaine , Holden Hall, Jeffery Li

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LIPIcs.FUN.2024.24.pdf
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MIT Hardness Group
  • CSAIL, Massachusetts Institute of Technology, Cambridge, MA, USA
Erik D. Demaine
  • CSAIL, Massachusetts Institute of Technology, Cambridge, MA, USA
Holden Hall
  • CSAIL, Massachusetts Institute of Technology, Cambridge, MA, USA
Jeffery Li
  • CSAIL, Massachusetts Institute of Technology, Cambridge, MA, USA

Acknowledgements

This paper was initiated during open problem solving in the MIT class on Algorithmic Lower Bounds: Fun with Hardness Proofs (6.5440) taught by Erik Demaine in Fall 2023. We thank the other participants of that class for helpful discussions and providing an inspiring atmosphere. Figures drawn with SVG Tiler (https://github.com/edemaine/svgtiler).

Cite As Get BibTex

MIT Hardness Group, Erik D. Demaine, Holden Hall, and Jeffery Li. Tetris with Few Piece Types. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 24:1-24:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.FUN.2024.24

Abstract

We prove NP-hardness and #P-hardness of Tetris clearing (clearing an initial board using a given sequence of pieces) with the Super Rotation System (SRS), even when the pieces are limited to any two of the seven Tetris piece types. This result is the first advance on a question posed twenty years ago: which piece sets are easy vs. hard? All previous Tetris NP-hardness proofs used five of the seven piece types. We also prove ASP-completeness of Tetris clearing, using three piece types, as well as versions of 3-Partition and Numerical 3-Dimensional Matching where all input integers are distinct. Finally, we prove NP-hardness of Tetris survival and clearing under the "hard drops only" and "20G" modes, using two piece types, improving on a previous "hard drops only" result that used five piece types.

Subject Classification

ACM Subject Classification
  • Theory of computation → Problems, reductions and completeness
Keywords
  • complexity
  • hardness
  • video games
  • counting

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References

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