Paper by Erik D. Demaine

Reference:

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.

Abstract:

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.

Comments:

This paper is also available as arXiv:2003.08331.

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Tatamibari Font