The fewest clues problem
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paper.pdf
Description
Accepted version
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560.68 KB
Format
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Author(s)
Demaine, Erik D
Ma, Fermi
Schvartzman, Ariel
Waingarten, Erik
Aaronson, Scott
Date Issued
November 2018
Journal
Theoretical Computer Science
Publisher
Elsevier BV
Citation
Demaine, Erik D. et al. "The fewest clues problem." Theoretical Computer Science 748 (November 2018): 28-39 © 2018 Elsevier B.V.
Version
Author's final manuscript
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 Σ2P-complete. Along the way, we show that the FCP versions of TRIANGLE PARTITION, PLANAR 1-IN-3 SAT, and LATIN SQUARE are all Σ2P-complete. We show that even problems in P have difficult FCP versions, sometimes even Σ2P-complete, though “closed under cluing” problems are in the (presumably) smaller class NP; for example, FCP 2SAT is NP-complete.
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-NonCommercial-NoDerivs License
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1016/j.tcs.2018.01.020
