Volume 4958 of the series Lecture Notes in Computer Science pp 372383
A Reasoning Framework for Solving Nonograms
 K. Joost BatenburgAffiliated withVision Lab, Department of Physics, University of Antwerp
 , Walter A. KostersAffiliated withLeiden Institute of Advanced Computer Science, Leiden University
Abstract
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 NPhard. 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, 2satisfiability 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.
 Title
 A Reasoning Framework for Solving Nonograms
 Book Title
 Combinatorial Image Analysis
 Book Subtitle
 12th International Workshop, IWCIA 2008, Buffalo, NY, USA, April 79, 2008. Proceedings
 Pages
 pp 372383
 Copyright
 2008
 DOI
 10.1007/9783540782759_33
 Print ISBN
 9783540782742
 Online ISBN
 9783540782759
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 4958
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
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 Editors
 Authors

 K. Joost Batenburg ^{(1)}
 Walter A. Kosters ^{(2)}
 Author Affiliations

 1. Vision Lab, Department of Physics, University of Antwerp, Belgium
 2. Leiden Institute of Advanced Computer Science, Leiden University, The Netherlands
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