Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Adler, Aviv; Bosboom, Jeffrey; Demaine, Erik D.; Demaine, Martin L.; Liu, Quanquan C.; Lynch, Jayson License: Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)
when quoting this document, please refer to the following
URN: urn:nbn:de:0030-drops-127624

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Tatamibari Is NP-Complete



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

  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 =		{},
  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

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