A Reasoning Framework for Solving Nonograms

  • K. Joost Batenburg
  • Walter A. Kosters
Conference paper

DOI: 10.1007/978-3-540-78275-9_33

Part of the Lecture Notes in Computer Science book series (LNCS, volume 4958)
Cite this paper as:
Batenburg K.J., Kosters W.A. (2008) A Reasoning Framework for Solving Nonograms. In: Brimkov V.E., Barneva R.P., Hauptman H.A. (eds) Combinatorial Image Analysis. IWCIA 2008. Lecture Notes in Computer Science, vol 4958. Springer, Berlin, Heidelberg


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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • K. Joost Batenburg
    • 1
  • Walter A. Kosters
    • 2
  1. 1.Vision Lab, Department of PhysicsUniversity of AntwerpBelgium
  2. 2.Leiden Institute of Advanced Computer ScienceLeiden UniversityThe Netherlands

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