Tatamibari is NPcomplete
Abstract
In the Nikoli pencilandpaper game Tatamibari, a puzzle consists of an $m \times n$ 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 NPcomplete, 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 NPhardness proof for Spiral Galaxies. We also present a mathematical puzzle font for Tatamibari.
 Publication:

arXiv eprints
 Pub Date:
 March 2020
 arXiv:
 arXiv:2003.08331
 Bibcode:
 2020arXiv200308331A
 Keywords:

 Computer Science  Computational Complexity;
 Computer Science  Computational Geometry
 EPrint:
 26 pages, 21 figures. New discussion of safe placement of wires in Sections 3.2 and 3.5. To appear at the 10th International Conference on Fun with Algorithms (FUN 2020)