License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SEA.2022.2
URN: urn:nbn:de:0030-drops-165366
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Ishihata, Masakazu ; Tokumasu, Fumiya

Solving and Generating Nagareru Puzzles

LIPIcs-SEA-2022-2.pdf (1 MB)


Solving paper-and-pencil puzzles is fun for people, and their analysis is also an essential issue in computational complexity theory. There are some practically efficient solvers for some NP-complete puzzles; however, the automatic generation of interesting puzzle instances still stands out as a complex problem because it requires checking whether the generated instance has a unique solution. In this paper, we focus on a puzzle called Nagareru and propose two methods: one is for implicitly enumerating all the solutions of its instance, and the other is for efficiently generating an instance with a unique solution. The former constructs a ZDD that implicitly represents all the solutions. The latter employs the ZDD-based solver as a building block to check the uniqueness of the solution of generated instances. We experimentally showed that the ZDD-based solver was drastically faster than a CSP-based solver, and our generation method created an interesting instance in a reasonable time.

BibTeX - Entry

  author =	{Ishihata, Masakazu and Tokumasu, Fumiya},
  title =	{{Solving and Generating Nagareru Puzzles}},
  booktitle =	{20th International Symposium on Experimental Algorithms (SEA 2022)},
  pages =	{2:1--2:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-251-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{233},
  editor =	{Schulz, Christian and U\c{c}ar, Bora},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-165366},
  doi =		{10.4230/LIPIcs.SEA.2022.2},
  annote =	{Keywords: Paper-and-pencil puzzle, SAT, CSP, ZDD}

Keywords: Paper-and-pencil puzzle, SAT, CSP, ZDD
Collection: 20th International Symposium on Experimental Algorithms (SEA 2022)
Issue Date: 2022
Date of publication: 11.07.2022
Supplementary Material: Software (Source Code and Data): archived at:

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