eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-09-16
1:1
1:24
10.4230/LIPIcs.FUN.2021.1
article
Tatamibari Is NP-Complete
Adler, Aviv
1
Bosboom, Jeffrey
1
Demaine, Erik D.
1
Demaine, Martin L.
1
Liu, Quanquan C.
1
Lynch, Jayson
1
Massachusetts Institute of Technology, Cambridge, MA, USA
In the Nikoli pencil-and-paper game Tatamibari, a puzzle consists of an m x 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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol157-fun2021/LIPIcs.FUN.2021.1/LIPIcs.FUN.2021.1.pdf
Nikoli puzzles
NP-hardness
rectangle covering