Paper by Erik D. Demaine
- Aviv Adler, Jeffrey Bosboom, Erik D. Demaine, Martin L. Demaine, Quanquan C. Liu, and Jayson Lynch, “Tatamibari is NP-complete”, in Proceedings of the 10th International Conference on Fun with Algorithms (FUN 2020), La Maddalena, Italy, September 28–30, 2020, 1:1–1:24.
In the Nikoli pencil-and-paper game Tatamibari, a puzzle consists of an
m × n grid of cells, where each cell possibly
contains a clue among +, −, |. The goal is to partition the grid into disjoint rectangles,
where every rectangle contains exactly one clue, rectangles containing + are square, rectangles containing − are strictly longer horizontally
than vertically, rectangles containing | are strictly longer vertically than horizontally, and no four
rectangles share a corner. We prove this puzzle NP-complete, establishing a
Nikoli gap of 16 years. Along the way, we introduce a gadget framework for
proving hardness of similar puzzles involving area coverage, and show that it
applies to an existing NP-hardness proof for Spiral Galaxies. We also present
a mathematical puzzle font for Tatamibari.
- This paper is also available as arXiv:2003.08331.
- The paper is available in PDF (1226k).
- See information on file formats.
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- Related webpages:
- Tatamibari Font
See also other papers by Erik Demaine.
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