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Solving and Generating Nagareru Puzzles

Authors Masakazu Ishihata, Fumiya Tokumasu

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Subject Classification

ACM Subject Classification
  • Computing methodologies → Combinatorial algorithms
  • Theory of computation → Generating random combinatorial structures
  • Mathematics of computing → Graph algorithms
Keywords
  • Paper-and-pencil puzzle
  • SAT
  • CSP
  • ZDD

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Abstract

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.

Cite As Get BibTex

Masakazu Ishihata and Fumiya Tokumasu. Solving and Generating Nagareru Puzzles. In 20th International Symposium on Experimental Algorithms (SEA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 233, pp. 2:1-2:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.SEA.2022.2

Author Details

Masakazu Ishihata
  • NTT Communication Science Laboratories, Kyoto, Japan
Fumiya Tokumasu
  • National Institute of Technology, Nara College, Nara, Japan

Supplementary Materials

References

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