LIPIcs.FUN.2024.25.pdf
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Complexity of Planar Graph Orientation Consistency, Promise-Inference, and Uniqueness, with Applications to Minesweeper Variants
Authors
Della Hendrickson 
,
Andy Tockman
-
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Volume:
12th International Conference on Fun with Algorithms (FUN 2024)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: International Conference on Fun with Algorithms (FUN) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2024-05-29
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Acknowledgements
This paper was initiated during open problem solving in the MIT class on Algorithmic Lower Bounds: Fun with Hardness Proofs (6.5440) taught by Erik Demaine in Fall 2023. We thank the other participants of that class for helpful discussions and providing an inspiring atmosphere.
Cite AsGet BibTex
MIT Hardness Group, Della Hendrickson, and Andy Tockman. Complexity of Planar Graph Orientation Consistency, Promise-Inference, and Uniqueness, with Applications to Minesweeper Variants. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 25:1-25:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.FUN.2024.25
https://doi.org/10.4230/LIPIcs.FUN.2024.25
Abstract
We study three problems related to the computational complexity of the popular game Minesweeper. The first is consistency: given a set of clues, is there any arrangement of mines that satisfies it? This problem has been known to be NP-complete since 2000 [Kaye, 2000], but our framework proves it as a side effect. The second is inference: given a set of clues, is there any cell that the player can prove is safe? The coNP-completeness of this problem has been in the literature since 2011 [Scott et al., 2011], but we discovered a flaw that we believe is present in all published results, and we provide a fixed proof. Finally, the third is solvability: given the full state of a Minesweeper game, can the player win the game by safely clicking all non-mine cells? This problem has not yet been studied, and we prove that it is coNP-complete.
Subject Classification
ACM Subject Classification
- Theory of computation → Problems, reductions and completeness
Keywords
- NP
- coNP
- hardness
- minesweeper
- solvability
- gadgets
- simulation
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References
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