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Passing Messages to Lonely Numbers
March/April 2008 (vol. 10 no. 2)
pp. 32-40
Heiko Bauke, Max Planck Institute for Nuclear Physics
Message-passing methods provide powerful approximation algorithms for problems that can be formulated in terms of (probabilistic) graphical models. These methods find applications in statistical physics, inference, and combinatorial optimization. Sudoku, a popular number puzzle, is a simple optimization problem that message-passing algorithms can help solve. Therefore, Sudoku is an ideal vehicle to demonstrate these methods' strengths and limitations.

1. B. Hayes, "Unwed Numbers," Am. Scientist, vol. 94, no. 1, 2006, pp. 12–15.
2. H. Simonis, "Sudoku as a Constrained Problem," Proc. 4th Int'l Workshop Modeling and Reformulating Constrained Satisfaction Problems, 2005, pp. 13–27.
3. I. Lynce and J. Ouaknine, "Sudoku as a SAT Problem," Proc. 9th Int'l Symp. Artificial Intelligence and Mathematics, 2006; http://anytime.cs.umass.edu/aimath06/proceedings P34.pdf.
4. F.R. Kschischang, B.J. Frey, and H.-A. Loeliger, "Factor Graphs and the Sum-Product Algorithm," IEEE Trans. Information Theory, vol. 47, no. 2, 2001, pp. 498–519.
5. M. Mézard, "Passing Messages between Disciplines," Science, vol. 301, no. 5640, 2003, pp. 1685–1686.
6. J.S. Yedidia, W.T. Freeman, and Y. Weiss, "Constructing Free Energy Approximations and Generalized Belief Propagation Algorithms," IEEE Trans. Information Theory, vol. 51, no. 7, 2005, pp. 2282–2312.
7. A. Pelizzola, "Cluster Variation Method in Statistical Physics and Probabilistic Graphical Models," J. Physics A, vol. 38, no. 33, 2005, pp. R309–339.
8. A. Braunstein, M. Mézard, and R. Zecchina, "Survey Propagation: An Algorithm for Satisfiability," Random Structures and Algorithms, vol. 27, no. 2, 2005, pp. 201–226.
9. A.K. Hartmann and M. Weigt, Phase Transitions in Combinatorial Optimization Problems: Basics, Algorithms and Statistical Mechanics, Wiley-VCH, 2005.
10. J. Goldberger, Solving Sudoku Using Combined Message Passing Algorithms, tech. report TR-BIU-ENG-2007-05-03, Eng. School, Bar-Ilan Univ., 2007; www.eng.biu.ac.il/~goldbej/papersSudoku_BP.pdf .

Index Terms:
computing, combinatorics, combinatorial, Sudoku, message passing, algorithms, combinatorics in computing
Citation:
Heiko Bauke, "Passing Messages to Lonely Numbers," Computing in Science and Engineering, vol. 10, no. 2, pp. 32-40, March-April 2008, doi:10.1109/MCSE.2008.60
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