Reconstructing convex polyominoes from horizontal and vertical projections
Theoretical Computer Science
Binary vectors partially determined by linear equation systems
Discrete Mathematics
The reconstruction of polyominoes from their orthogonal projections
Information Processing Letters
Reconstruction of convex 2D discrete sets in polynomial time
Theoretical Computer Science
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Artificial Intelligence: A Modern Approach
Artificial Intelligence: A Modern Approach
Advances in Discrete Tomography and Its Applications (Applied and Numerical Harmonic Analysis)
Advances in Discrete Tomography and Its Applications (Applied and Numerical Harmonic Analysis)
A Network Flow Algorithm for Reconstructing Binary Images from Discrete X-rays
Journal of Mathematical Imaging and Vision
Technical Section: Automated generation and visualization of picture-logic puzzles
Computers and Graphics
A unified theory of structural tractability for constraint satisfaction problems
Journal of Computer and System Sciences
Theoretical Computer Science
A reasoning framework for solving nonograms
IWCIA'08 Proceedings of the 12th international conference on Combinatorial image analysis
Teaching Advanced Features of Evolutionary Algorithms Using Japanese Puzzles
IEEE Transactions on Education
Solving Japanese nonograms by Taguchi-based genetic algorithm
Applied Intelligence
An evolutionary-based hyper-heuristic approach for the Jawbreaker puzzle
Applied Intelligence
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Nonograms, also known as Japanese puzzles, are a specific type of logic drawing puzzles. The challenge is to fill a grid with black and white pixels in such a way that a given description for each row and column, indicating the lengths of consecutive segments of black pixels, is adhered to. Although the Nonograms in puzzle books can usually be solved by hand, the general problem of solving Nonograms is NP-hard. In this paper, we propose a reasoning framework that can be used to determine the value of certain pixels in the puzzle, given a partial filling. Constraints obtained from relaxations of the Nonogram problem are combined into a 2-Satisfiability (2-SAT) problem, which is used to deduce pixel values in the Nonogram solution. By iterating this procedure, starting from an empty grid, it is often possible to solve the puzzle completely. All the computations involved in the solution process can be performed in polynomial time. Our experimental results demonstrate that the approach is capable of solving a variety of Nonograms that cannot be solved by simple logic reasoning within individual rows and columns, without resorting to branching operations. In addition, we present statistical results on the solvability of Nonograms, obtained by applying our method to a large number of Nonograms.