A Survey of Np-Complete Puzzles

Kendall, Graham; Parkes, Andrew J.; Spoerer, Kristian

doi:10.3233/icg-2008-31103

Cited by 105 publications

(82 citation statements)

References 49 publications

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“…Interestingly, despite its widespread appeal, Tetris is unwinnable. If you play it long enough, you will lose (Baccherini & Donatella, 2008;Kendall et al, 2008;Fahey, 2013)! There are seven unique shapes for zoids, one for each permutation of four contiguous block segments.…”

Section: Rules Of Tetrismentioning

confidence: 99%

Meta-T: TetrisⓇ as an experimental paradigm for cognitive skills research

Lindstedt

Gray

2015

Behav Res

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Studies of human performance in complex tasks using video games are an attractive prospect, but many existing games lack a comprehensive way to modify the game and track performance beyond basic levels of analysis. Meta-T provides experimenters a tool to study behavior in a dynamic task environment with time-stressed decisionmaking and strong perceptual-motor elements, offering a host of experimental manipulations with a robust and detailed logging system for all user events, system events, and screen objects. Its experimenter-friendly interface provides control over detailed parameters of the task environment without need for programming expertise. Support for eye-tracking and computational cognitive modeling extend the paradigm's scope.

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Section: Rules Of Tetrismentioning

confidence: 99%

Meta-T: TetrisⓇ as an experimental paradigm for cognitive skills research

Lindstedt

Gray

2015

Behav Res

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“…Amongst other games to have been proved NP-complete or harder are the card solitaire games Klondike (Longpré & McKenzie, 2009), Freecell (Helmert, 2003) and Black Hole (Gent, Jefferson, Kelsey, Lynce, Miguel, Nightingale, Smith, & Tarim, 2007), the Sudoku puzzle (Takayuki & Takahiro, 2003), video games like Pac-Man (Viglietta, 2014), and casual games such as Minesweeper (Kaye, 2000), Candy Crush Saga and Bejeweled (Walsh, 2014;Guala, Leucci, & Natale, 2014). Many other games are surveyed by Kendall, Parkes, and Spoerer (2008) and by Demaine and Hearn (2009). In each case, the complexitytheorist must define a generalised class of instances.…”

Section: Introductionmentioning

confidence: 99%

Complexity of n-Queens Completion

Gent

Jefferson

Nightingale

2017

jair

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The n-Queens problem is to place n chess queens on an n by n chessboard so that no two queens are on the same row, column or diagonal. The n-Queens Completion problem is a variant, dating to 1850, in which some queens are already placed and the solver is asked to place the rest, if possible. We show that n-Queens Completion is both NP-Complete and #P-Complete. A corollary is that any non-attacking arrangement of queens can be included as a part of a solution to a larger n-Queens problem. We introduce generators of random instances for n-Queens Completion and the closely related Blocked n-Queens and Excluded Diagonals Problem. We describe three solvers for these problems, and empirically analyse the hardness of randomly generated instances. For Blocked n-Queens and the Excluded Diagonals Problem, we show the existence of a phase transition associated with hard instances as has been seen in other NP-Complete problems, but a natural generator for n-Queens Completion did not generate consistently hard instances. The significance of this work is that the n-Queens problem has been very widely used as a benchmark in Artificial Intelligence, but conclusions on it are often disputable because of the simple complexity of the decision problem. Our results give alternative benchmarks which are hard theoretically and empirically, but for which solving techniques designed for n-Queens need minimal or no change.

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“…The meta-puzzle for us theoretical computer scientists is to study the computational complexity of puzzles, characterizing them as polynomially solvable, NP-complete, or harder [7]. In the case of Nikoli puzzles, nearly every family has been proved NP-complete: Country Road [10], Corral [5], Fillomino [29], Hiroimono [1], Hashiwokakero [2], Heyawake [9], Kakuro [24], Kurodoko [15], Light Up [21], Masyu [6], Nurikabe ( [8], [20], [22]), Shakashaka [3], Slither Link ( [28], [29]), Sudoku ( [14], [29], [30]), Yajilin [10], and Yosenabe [12].…”

Section: Introductionmentioning

confidence: 99%

Zig-Zag Numberlink is NP-Complete

Adcock

Demaine

et al. 2015

Journal of Information Processing

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When can t terminal pairs in an m × n grid be connected by t vertex-disjoint paths that cover all vertices of the grid? We prove that this problem is NP-complete. Our hardness result can be compared to two previous NPhardness proofs: Lynch's 1975 proof without the "cover all vertices" constraint, and Kotsuma and Takenaga's 2010 proof when the paths are restricted to have the fewest possible corners within their homotopy class. The latter restriction is a common form of the famous Nikoli puzzle Numberlink. Our problem is another common form of Numberlink, sometimes called Zig-Zag Numberlink and popularized by the smartphone app Flow Free.

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A Survey of Np-Complete Puzzles

Cited by 105 publications

References 49 publications

Meta-T: TetrisⓇ as an experimental paradigm for cognitive skills research

Meta-T: TetrisⓇ as an experimental paradigm for cognitive skills research

Complexity of n-Queens Completion

Zig-Zag Numberlink is NP-Complete

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