Tatamibari is NP-complete
Name
LIPIcs-FUN-2021-1.pdf
Description
Published version
Size
1.21 MB
Format
Adobe PDF
Checksum (MD5)
1698e1fc974b2d6036b26356b3139f8c
Author(s)
Adler, Aviv
Bosboom, Jeffrey William
Demaine, Erik D
Demaine, Martin L
Liu, Quanquan C.
Lynch, Jayson R.
Date Issued
March 2020
Journal
10th International Conference on Fun with Algorithms
Publisher
Schloss Dagstuhl, Leibniz Center for Informatics
Citation
Adler, Aviv et al. “Tatamibari is NP-complete.” 10th International Conference on Fun with Algorithms, May-June 2021, Favignana Island, Italy, Schloss Dagstuhl and Leibniz Center for Informatics, 2021. © 2021 The Author(s)
Version
Final published version
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.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Terms of Use
Creative Commons Attribution 3.0 unported license
Persistent DSpace Link
DOI of Published Version
10.4230/LIPIcs.FUN.2021.1
