Solving the Slitherlink Problem

Liu, Tung-Ying; Wu, I‐Chen; Sun, Der-Johng

doi:10.1109/taai.2012.36

Cited by 4 publications

(3 citation statements)

References 3 publications

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“…The FP method proposed in this paper is actually a generic method for many puzzle problems. In practice, we are applying this method to some other puzzle problems such as Nurikabe [22], Slitherlink [12], and Sudoku [11]. We believe this method is an important generic method for solving puzzles like dancing links [9].…”

Section: Discussionmentioning

confidence: 99%

An Efficient Approach to Solving Nonograms

Sun

Chen

et al. 2013

IEEE Trans. Comput. Intell. AI Games

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A nonogram puzzle is played on a rectangular grid of pixels with clues given in the form of row and column constraints. The aim of solving a nonogram puzzle, an NP-complete problem, is to paint all the pixels of the grid in black and white while satisfying these constraints. This paper proposes an efficient approach to solving nonogram puzzles. We propose a fast dynamic programming (DP) method for line solving, whose time complexity in the worst case is only, where the grid size is and is the average number of integers in one constraint, always smaller than . In contrast, the time complexity for the best line-solving method in the past is . We also propose some fully probing (FP) methods to solve more pixels before running backtracking. Our FP methods can solve more pixels than the method proposed by Batenburg and Kosters (before backtracking), while having a time complexity that is smaller than theirs by a factor of . Most importantly, these FP methods provide useful guidance in choosing the next promising pixel to guess during backtracking. The proposed methods are incorporated into a fast nonogram solver, named LalaFrogKK. The program outperformed all the programs collected in webpbn.com, and also won both nonogram tournaments that were held at the 2011 Conference on Technologies and Applications of Artificial Intelligence (TAAI 2011, Taiwan). We expect that the proposed FP methods can also be applied to solving other puzzles efficiently.

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Section: Discussionmentioning

confidence: 99%

An Efficient Approach to Solving Nonograms

Sun

Chen

et al. 2013

IEEE Trans. Comput. Intell. AI Games

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“…An example Slitherlink instance is shown in Figure 6 (left), with its solution also shown. The problem of finding a solution to Slitherlink is NP-complete [10], [41], and a small number of algorithms for its solution have been proposed [42], [43].…”

Section: E Slitherlinkmentioning

confidence: 99%

J-POP: Japanese Puzzles as Optimization Problems

et al. 2022

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Japanese puzzle games such as Sudoku and Futoshiki are familiar recreational pursuits, but they also present an interesting computational challenge. A number of algorithms exist for the automated solution of such puzzles, but, until now, these have not been compared in a unified way. Here we present an integrated framework for the study of combinatorial blackbox optimisation, using Japanese puzzles as the test-bed. Importantly, our platform is extendable, allowing for the easy addition of both puzzles and solvers. We compare the performance of a number of optimization algorithms on five different puzzle games, and identify a subset of puzzle instances that could provide a challenging benchmark set for future algorithms.

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“…Examples of gridbased puzzles include: Sudoku and its variants (Arnold et al 2012), Slitherlink (Liu, 2012), PegSolitaire (Ravikumar et al, 2004), Blocks (Slaney and Thiebaux, 2001), Mastermind (Stuckman and Zhang, 2006). Many methodologies and algorithms for solving various grid-based puzzles have also been proposed (Ortiz-García et al 2008), (Batenburg and Kosters, 2004), (Wiggers, 2004), (Salcedo-Sanz et al 2007).…”

Section: Introductionmentioning

confidence: 99%

Solving Kakuro Puzzle using Self Adapting Harmony Search Metaheuristic Algorithm

Panov¹,

Koceski²

2014

International Journal of Engineering Practical Research

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In paper presents a Self Adapting Harmony Search (SAHS) metahauristic based solution to the grid-based Japaneese game know as Kakuro. It has been shown that our approach can provide a time-efficient solution to obtaining a correct positioning of the numbers in the cells of a puzzle, with proper previous filtering of the combination of the numbers in the sets of sums. The pre-computation phase has given great improvements to the SAHS algorithm in order to reduce the search space. The proposed solution has been experimentally evaluated on various grids with different size and the results shown that the algorithm is very robust and always converged to the solution.

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Solving the Slitherlink Problem

Cited by 4 publications

References 3 publications

An Efficient Approach to Solving Nonograms

An Efficient Approach to Solving Nonograms

J-POP: Japanese Puzzles as Optimization Problems

Solving Kakuro Puzzle using Self Adapting Harmony Search Metaheuristic Algorithm

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