Entropy landscape and non-Gibbs solutions in constraint satisfaction problems

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 77, Issue 3, 2008, Pages

  Dall'asta, L ^a   Ramezanpour, A ^a   Zecchina, R ^b  

^a ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS   (Italy)

^b POLITECNICO DI TORINO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; PROBLEM SOLVING; RANDOM PROCESSES; THERMODYNAMIC PROPERTIES;

BICOLORING PROBLEM; CAVITY METHOD; CONSTRAINT SATISFACTION PROBLEM; ENTROPY LANDSCAPE;

GRAPH THEORY;

EID: 41149176981     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.77.031118     Document Type: Article

References (41)

1. R. G. Gallager, Information Theory and Reliable Communication (Wiley, New York, 1968).
2. D. J. C. MacKay, Information Theory, Inference and Learning Algorithms (Cambridge University Press, Cambridge, England, 2002).
3. NP-hardness and Phase Transitions, edited by O. Dubois, R. Monasson, B. Selman, and R. Zecchina
4. [Theor. Comput. Sci. TCSCDI 0304-3975 265 (1-2) (2001)].
5. D. Challet, M. Marsili, and R. Zecchina, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.1824 84, 1824 (2000).
6. T. Galla, M. Leone, M. Marsili, M. Sellitto, M. Weigt, and R. Zecchina, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.128701 97, 128701 (2006).
7. A. Braunstein and R. Zecchina, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.030201 96, 030201 (2006).
8. C. Baldassi, A. Braunstein, N. Brunel, and R. Zecchina, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 10.1073/pnas.0700324104 104, 11079 (2007).
9. S. Cook, in Proceedings of the Third Annual ACM Symposium on Theory of Computing (ACM, Ohio, 1971), pp. 151-158.
10. M. Garey and D. Johnson, Computers and Intractability A Guide to the Theory of NP-completeness (Freeman, San Francisco, 1979).
11. S. Kirkpatrick and B. Selman, Science SCIEAS 0036-8075 10.1126/science.264.5163.1297 264, 1297 (1994).
12. R. Monasson, R. Zecchina, S. Kirkpatrick, B. Selman, and L. Troyanski, Nature (London) NATUAS 0028-0836 10.1038/22055 400, 133 (1999).
13. M. Mézard, F. Ricci-Tersenghi, and R. Zecchina, J. Stat. Phys. JSTPBS 0022-4715 10.1023/A:1022886412117 111, 505 (2003).
14. S. Cocco, O. Dubois, J. Mandler, and R. Monasson, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.047205 90, 047205 (2003).
15. M. Mézard, M. Palassini, and O. Rivoire, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.200202 95, 200202 (2005).
16. T. Mora, Ph.D. thesis, LPTMS Université Paris-Sud, 2007 (unpublished).
17. F. Krzakala, A. Montanari, F. Ricci-Tersenghi, G. Semerjian, and L. Zdeborova, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 10.1073/pnas. 0703685104 104, 10318 (2007).
18. L. Zdeborova and F. Krzakala, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.76.031131 76, 031131 (2007).
19. G. Semerjian, J. Stat. Phys. JSTPBS 0022-4715 10.1007/s10955-007-9417-7 130, 251 (2008).
20. F. Krzakala and J. Kurchan, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.76.021122 76, 021122 (2007).
21. R. Monasson and R. Zecchina, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.56.1357 56, 1357 (1997).
22. M. Mézard, G. Parisi, and R. Zecchina, Science SCIEAS 0036-8075 10.1126/science.1073287 297, 812 (2002).
23. M. Mézard and R. Zecchina, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.66.056126 66, 056126 (2002).
24. R. Mulet, A. Pagnani, M. Weigt, and R. Zecchina, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.89.268701 89, 268701 (2002).
25. D. Achlioptas, A. Naor, and Y. Peres, Nature (London) NATUAS 0028-0836 10.1038/nature03602 435, 759 (2005).
26. S. Mertens, M. Mézard, and R. Zecchina, Random Struct. Algorithms RSALFD 1042-9832 10.1002/rsa.20090 28, 340 (2006).
27. M. Mezard, G. Parisi, and M. A. Virasoro, Spin-Glass Theory and Beyond, Vol. 9 of Lecture Notes in Physics (World Scientific, Singapore, 1987).
28. M. Mézard and G. Parisi, Eur. Phys. J. B EPJBFY 1434-6028 10.1007/PL00011099 20, 217 (2001).
29. M. Mézard and G. Parisi, J. Stat. Phys. JSTPBS 0022-4715 10.1023/A:1022221005097 111, 1 (2003).
30. O. Rivoire, J. Stat. Mech.: Theory Exp. ZZZZZZ 1742-5468 (2005), P07004.
31. F. R. Kschischang, B. J. Frey, and H.-A. Loeliger, IEEE Trans. Inf. Theory IETTAW 0018-9448 10.1109/18.910572 47, 498 (2001).
32. E. Friedgut, J. Am. Math. Soc. 12, 1017 (1999). 0894-0347
33. T. Castellani, V. Napolano, F. Ricci-Tersenghi, and R. Zecchina, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/36/43/026 36, 11037 (2003).
34. A. Braunstein, M. Mezard, and R. Zecchina, Random Struct. Algorithms RSALFD 1042-9832 10.1002/rsa.20057 27, 201 (2005).
35. A. Braunstein, F. Kahyan, G. Montorsi, and R. Zecchina, in Encoding for the Blackwell Channel with Reinforced Belief Propagation, Proceedings of the IEEE International Symposium on Information Theory (IEEE, Nice, France, 2007).
36. S. Seitz, M. Alava, and P. Orponen, J. Stat. Mech.: Theory Exp. ZZZZZZ 1742-5468 (2005), P06006.
37. T. Mora and M. Mézard, J. Stat. Mech.: Theory Exp. ZZZZZZ 1742-5468 (2005), P10007.
38. G. Parisi (unpublished).
39. D. Achlioptas and F. Ricci-Tersenghi, in Proceedings of the 38th Annual ACM Symposium on Theory of Computing (ACM, Seattle., 2006), Session 4A, p. 130.
40. A. Montanari and F. Ricci-Tersenghi, Eur. Phys. J. B EPJBFY 1434-6028 10.1140/epjb/e2003-00174-7 33, 339 (2003).
41. A. Montanari, G. Parisi, and F. Ricci-Tersenghi, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/37/6/008 37, 2073 (2004).