Paper by Erik D. Demaine

Reference:

MIT Hardness Group, Erik D. Demaine, Holden Hall, and Jeffery Li, “Tetris with Few Piece Types”, in Proceedings of the 12th International Conference on Fun with Algorithms (FUN 2024), edited by Andrei Z. Broder and Tami Tamir, LIPIcs, volume 291, La Maddalena, Italy, June 4–8, 2024, 24:1–24:18.

BibTeX

@InProceedings{TetrisPieces_FUN2024,
  key           = {MIT},
  AUTHOR        = {{MIT Hardness Group} and Erik D. Demaine and Holden Hall and Jeffery Li},
  TITLE         = {Tetris with Few Piece Types},
  BOOKTITLE     = {Proceedings of the 12th International Conference on Fun with Algorithms (FUN 2024)},
  bookurl       = {https://sites.google.com/unipi.it/fun2024},
  EDITOR        = {Andrei Z. Broder and Tami Tamir},
  SERIES        = {LIPIcs},
  VOLUME        = 291,
  ADDRESS       = {La Maddalena, Italy},
  MONTH         = {June 4--8},
  YEAR          = 2024,
  PAGES         = {24:1--24:18},

  withstudent   = 1,
  length        = {18 pages},
  updates       = {See <A HREF="https://www.youtube.com/watch?v=qhpcgu7-AT0&list=PLCZQ5yzonfsb6jy_QiUxrvXQDwmAbZX-8">videos of the gadgets in action</A>.},
  papers        = {TetrisPieces_TCS},
  doi           = {https://dx.doi.org/10.4230/LIPIcs.FUN.2024.24},
  dblp          = {https://dblp.org/rec/conf/fun/GroupDHL24},
  comments      = {This paper is also available from <A HREF="https://doi.org/10.4230/LIPIcs.FUN.2024.24">LIPIcs</A> and as <A HREF="https://arXiv.org/abs/2404.10712">arXiv:2404.10712</A>.},
}

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.

Comments:

This paper is also available from LIPIcs and as arXiv:2404.10712.

Updates:

See videos of the gadgets in action.

Length:

The paper is 18 pages.

Availability:

The paper is available in PDF (944k).

See information on file formats.

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Related papers:

TetrisPieces_TCS (Tetris with Few Piece Types)