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DOI: 10.4230/LIPIcs.FUN.2021.1
URN: urn:nbn:de:0030-drops-127624
URL: https://drops.dagstuhl.de/opus/volltexte/2020/12762/
Adler, Aviv ; Bosboom, Jeffrey ; Demaine, Erik D. ; Demaine, Martin L. ; Liu, Quanquan C. ; Lynch, Jayson
Tatamibari Is NP-Complete
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Abstract
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.
BibTeX - Entry
@InProceedings{adler_et_al:LIPIcs:2020:12762,
author = {Aviv Adler and Jeffrey Bosboom and Erik D. Demaine and Martin L. Demaine and Quanquan C. Liu and Jayson Lynch},
title = {{Tatamibari Is NP-Complete}},
booktitle = {10th International Conference on Fun with Algorithms (FUN 2021)},
pages = {1:1--1:24},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-145-0},
ISSN = {1868-8969},
year = {2020},
volume = {157},
editor = {Martin Farach-Colton and Giuseppe Prencipe and Ryuhei Uehara},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2020/12762},
URN = {urn:nbn:de:0030-drops-127624},
doi = {10.4230/LIPIcs.FUN.2021.1},
annote = {Keywords: Nikoli puzzles, NP-hardness, rectangle covering}
}
| Keywords: | Nikoli puzzles, NP-hardness, rectangle covering | |
| Seminar: | 10th International Conference on Fun with Algorithms (FUN 2021) | |
| Issue date: | 2020 | |
| Date of publication: | 16.09.2020 | |
| Supplementary Material: | The Z3-based Tatamibari solver and figures from Tatamibari NP-hardness paper are available at https://github.com/jbosboom/tatamibari-solver. |
