The chaos within sudoku

Scientific Reports

Volumn 2, Issue , 2012, Pages

  Ercsey Ravasz, Mária ^a   Toroczkai, Zoltán ^b  

^a BABE BOLYAI UNIVERSITY   (Romania)

^b UNIVERSITY OF NOTRE DAME   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84868276797     PISSN: None     EISSN: 20452322     Source Type: Journal    
DOI: 10.1038/srep00725     Document Type: Article

References (33)

1. Rosenhouse, J. & Taalman, L. Taking Sudoku Seriously: The Math Behind the World's most Popular Pencil Puzzle (Oxford University Press, New York, 2011).
2. Garey, M. R. & Johnson, D.S.Computers and Intractability: A Guide tothe Theory of NP-Completeness (W. H. Freeman & Co., New York, NY, USA, 1990).
3. Karp, R. M. Reducibility among combinatorial problems. In Complexity of Computer Computations., R.E. Miller and J.W. Thatcher (editors). Proc. of a Symp. on the Complexity of Computer Computations. (New York: Plenum. pp. 85-103, 1972).
4. Yato, T. & Seta, T. Complexity and completeness of finding another solution and its application to puzzles. IEICE Trans. Fundamentals E86-A(5), 1052-1060 (2003).
5. Fortnow, L. The status of the P versus NP problem. Commun. ACM 52, 78-86 (2009).
6. Barahona, F. On the computational complexity of Ising spin glass models. J. Phys. A: Math. Gen. 15, 3241-3253 (1982).
7. Istrail, S. Statistical Mechanics, Three-Dimensionality and NP-Completeness: I. Universality of Intractability of the Partition Functions of the Ising Model Across Non-Planar Lattices. Proceedings of the 32nd ACM Symposium on the Theory of Computing (STOC00), ACM Press, pp. 87-96 (2000)
8. Brueggemann, T. & Kern, W. An improved local search algorithm for 3-SAT. Theor. Comp. Sci. 329(1-3), 303313 (2004).
9. Ott, E. Chaos in Dynamical Systems 2nd edn (Cambridge Univ. Press, 2002).
10. Cencini, M., Cecconi, F. & Vulpiani, A. Chaos: from simple models to complex systems (World Scientific, Singapore, 2009).
11. Lai, Y.-C. & Tél, T. Transient Chaos: Complex Dynamics on Finite-Time Scales (Springer 2011).
12. Cvitanović, P., Artuso, R., Mainieri, R. Tanner, G. & Vattay, G. Chaos: Classical and Quantum, ChaosBook.org/version13 (Niels Bohr Institute, Copenhagen 2010).
13. Tél, T. & Gruiz, T. Chaotic dynamics: And introduction. (Cambridge University Press, 2006).
14. Elser, V., Rankenburg, I. & Thibault, P. Searching with iterated maps. Proc. Natl. Acad. Sci. USA 104, 418-423 (2007). (Pubitemid 46123041)
15. Ercsey-Ravasz, M. & Toroczkai, Z. Optimization hardness as transient chaos in an analog approach to constraint satisfaction. Nature Physics 7, 966-970 (2011).
16. Kadanoff, L. P. & Tang, C. Escape from strange repellers. Proc. Natl Acad. Sci. 81, 1276-1279 (1984).
17. Tél, T. & Lai, Y-C. Chaotic transients in spatially extended systems. Phys. Rep. 460, 245-275 (2008).
18. Zdeborová, L. & Mézard, M. Locked constraint satisfaction problems. Phys. Rev. Lett. 101, 078702 (2008).
19. Zdeborová, L. & Mézard, M. Constraint satisfaction problems with isolated solutions are hard. J. Stat. Mech.: Theor. Exp. P12004 (2008).
20. http://www.sudokuoftheday.co.uk (accessed on 26-07-2012)
21. http://forum.enjoysudoku.com/the-hardest-sudokus-new-thread-t6539.html (accessed on 23-07-2012).
22. http://wiki.karadimov.info/index.php/Sudoku-algorithms#Exceptionally- difficult-Sudokus-.28h (accessed on 25-07-2012).
23. http://en.wikipedia.org/wiki/Algorithmics-of-sudoku#Exceptionally- difficult- Sudokus-.28hard (accessed on 27-07-2012).
24. http://www.youtube.com/watch?v5y4-aSLP9g-w (accessed on 19-06-2012).
25. http://www.extremesudoku.info/sudoku.html (accessed on 26-07-2012).
26. http://cavemancircus.com/2009/11/05/the-hardest-sudoku-puzzle-ever/ (accessed on 26-07-2012).
27. Hutchinson, P. The world's hardest Sudoku? The Guardian, August 22 (2010) http://www.guardian.co.uk/media/2010/aug/22/worlds-hardest-sudoku (accessed on 21-07-2012).
28. http://www.usatoday.com/news/offbeat/2006-11-06-sudoku-x.htm (accessed on 26-07-2012).
29. Eppstein, D. Solving Single-digit Sudoku Subproblems, http://arxiv.org/abs/1202.5074v2
30. McGuire, G., Tugeman, B. & Civario, G. There is no 16-Clue Sudoku: Solving the Sudoku Minimum Number of Clues Problem. http://arxiv.org/abs/1201. 0749 (accessed on 25-07-2012).
31. http://mapleta.maths.uwa.edu.au/gordon/sudokumin.php (accessed on 26-07-2012).
32. http://en.wikipedia.org/wiki/File:Symmetrical-18-clue-sudoku-01.JPG (accessed on 15-07-2012).
33. http://www.flickr.com/photos/npcomplete/3603730706/(accessed on 24-06-2012).