The fewest clues problem
Name
The fewest clues problem.pdf
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585.32 KB
Format
Adobe PDF
Checksum (MD5)
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Author(s)
Fermi, Ma
Schvartzman, Ariel
Waingarten, Erik
Demaine, Erik D
Aaronson, Scott
Date Issued
June 2016
Journal
Leibniz International Proceedings in Informatics
Publisher
Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik
Citation
Demaine, Erik D., et al. "The Fewest Clues Problem." 8th International Conference on Fun with Algorithms (FUN 2016), 8-10 June, 2016, La Maddalena, Italy, Dagstuhl Publishing, 2016.
Version
Final published version
Abstract
When analyzing the computational complexity of well-known puzzles, most papers consider the algorithmic challenge of solving a given instance of (a generalized form of) the puzzle. We take a different approach by analyzing the computational complexity of designing a "good" puzzle. We assume a puzzle maker designs part of an instance, but before publishing it, wants to ensure that the puzzle has a unique solution. Given a puzzle, we introduce the FCP (fewest clues problem) version of the problem: Given an instance to a puzzle, what is the minimum number of clues we must add in order to make the instance uniquely solvable? We analyze this question for the Nikoli puzzles Sudoku, Shakashaka, and Akari. Solving these puzzles is NP-complete, and we show their FCP versions are Sigma_2^P-complete. Along the way, we show that the FCP versions of 3SAT, 1-in-3SAT, Triangle Partition, Planar 3SAT, and Latin Square are all Sigma_2^P-complete. We show that even problems in P have difficult FCP versions, sometimes even Sigma_2^P-complete, though "closed under cluing" problems are in the (presumably) smaller class NP; for example, FCP 2SAT is NP-complete. Keywords and phrases: computational complexity, pencil-and-paper puzzles, hardness reductions
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution 4.0 International License
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.4230/LIPIcs.FUN.2016.12
