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
A Network Flow Algorithm for Reconstructing Binary Images from Discrete X-rays
Journal of Mathematical Imaging and Vision
Solving Nonograms by combining relaxations
Pattern Recognition
Solving Japanese nonograms by Taguchi-based genetic algorithm
Applied Intelligence
| Hi-index | 0.01 |
Nonograms, also known as Japanese puzzles, are logic puzzles that are sold by many news paper vendors. 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 local reasoning framework that can be used to deduce the value of certain pixels in the puzzle, given a partial filling. By iterating this procedure, starting from an empty grid, it is often possible to solve the puzzle completely. Our approach is based on ideas from dynamic programming, 2-satisfiability problems, and network flows. 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. Moreover, all the computations involved in the solution process can be performed in polynomial time.