Clusters of solutions and replica symmetry breaking in random k-satisfiability

Journal of Statistical Mechanics: Theory and Experiment

Volumn 2008, Issue 4, 2008, Pages

  Montanari, Andrea ^a,b   Ricci Tersenghi, Federico ^c   Semerjian, Guilhem ^d  

^a Stanford University   (United States)

^b STANFORD UNIVERSITY   (United States)

^c UNIVERSITÀ DI ROMA LA SAPIENZA   (Italy)

^d SORBONNE UNIVERSITÉ   (France)

Author keywords

Cavity and replica method; Disordered systems (theory); Message passing algorithms; Networks; Random graphs

Indexed keywords

EID: 43049118973     PISSN: 17425468     EISSN: 17425468     Source Type: Journal    
DOI: 10.1088/1742-5468/2008/04/P04004     Document Type: Article

References (59)

1. Garey M R and Johnson D S 1983 Computers and Intractability, A Guide to the Theory of NP-Completeness (San Francisco, CA: Freeman)
2. Mitchell D, Selman B and Levesque H 1992 Proc. 10th Nat. Conf. Artif. Intell. p459
3. Friedgut E 1999 J. Am. Math. Soc. 12 1017
4. Franco J 2001 Theor. Comput. Sci. 265 147
5. Dubois O 2001 Theor. Comput. Sci. 265 187
6. Achlioptas D and Peres Y 2004 J. Am. Math. Soc. 17 947
7. Fernandez de la Vega W 2001 Theor. Comput. Sci. 265 131
8. Monasson R and Zecchina R 1997 Phys. Rev. E 56 1357
9. Biroli G, Monasson R and Weigt M 2000 Eur. Phys. J. B 14 551
10. Mézard M and Zecchina R 2002 Phys. Rev. E 66 056126
11. Mézard M, Parisi G and Zecchina R 2002 Science 297 812
12. Mertens S, Mézard M and Zecchina R 2006 Random Struct. Algorithms 28 340
13. Mézard M, Parisi G and Virasoro M A 1987 Spin Glass Theory and Beyond (Singapore: World Scientific)
14. Krzakala F, Montanari A, Ricci-Tersenghi F, Semerjian G and Zdeborov L 2007 Proc. Nat. Acad. Sci. 104 10318
15. Zdeborov L and Krzakala F 2007 Phys. Rev. E 76 031131
16. Zhou H 2008 Preprint 0801.0205
17. Dall'Asta L, Ramezanpour A and Zecchina R 2008 Preprint 0801.2890
18. Talagrand M 2003 Spin Glasses: A Challenge for Mathematicians (Berlin: Springer)
19. Kschischang F, Frey B J and Loeliger H-A 2001 IEEE Trans. Inf. Theory 47 498
20. Georgii H O 1988 Gibbs Measures and Phase Transitions (Berlin: De Gruyter)
21. Parisi G 2003 Slow Relaxations and Nonequilibrium Dynamics in Condensed Matter (Les Houches Lecture Notes, Session LXXVII) ed J-L Barrat et al (Berlin: Springer) p271
22. Cugliandolo L F 2003 Slow Relaxations and Nonequilibrium Dynamics in Condensed Matter (Les Houches Lecture Notes, Session LXXVII) ed J-L Barrat et al (Berlin: Springer) p367
23. Monasson R 1995 Phys. Rev. Lett. 75 2847
24. Ruelle D 1987 Commun. Math. Phys. 108 225
25. Mézard M and Parisi G 2001 Eur. Phys. J. B 20 217
26. Mézard M and Montanari A 2006 J. Stat. Phys. 124 1317
27. Biroli G and Bouchaud J P 2004 J. Chem. Phys. 121 7347
28. Martinelli F, Sinclair A and Weitz D 2004 Commun. Math. Phys. 250 301
29. Cavagna A, Grigera T S and Verrocchio P 2007 Phys. Rev. Lett. 98 187801
30. Franz S and Parisi G 1995 J. Physique 5 1401
31. Berger E N, Kenyon C, Mossel E and Peres Y 2005 Probab. Theory Relat. Fields 131 311
32. Montanari A and Semerjian G 2006 J. Stat. Phys. 125 23
33. Mézard M, Palassini M and Rivoire O 2005 Phys. Rev. Lett. 95 200202
34. Mézard M and Parisi G 2003 J. Stat. Phys. 111 1
35. Daudé H, Mézard M, Mora T and Zecchina R 2008 Theor. Comput. Sci. 393 260
36. Achlioptas D and Ricci-Tersenghi F 2006 Proc. 38th ACM Symp. on Theory of Computing p130
37. Mora T and Zdeborova L 2007 Preprint 0710.3804
38. Mézard M, Ricci-Tersenghi F and Zecchina R 2003 J. Stat. Phys. 111 505
39. Cocco S, Dubois O, Mandler J and Monasson R 2003 Phys. Rev. Lett. 90 047205
40. Janson S, Luczak T and Rucinski A 2000 Random Graphs (New York: Wiley)
41. Mézard M and Montanari A 2008 Information, Physics, Computation: Probabilistic Approaches at press available at http://www.stanford.edu/ ∼montanar/BOOK/book.html
42. Franz S and Leone M 2003 J. Stat. Phys. 111 535
43. Panchenko D and Talagrand M 2004 Probab. Theory Relat. Fields 130 319
44. Montanari A and Shah D 2007 Proc. XVIII Symp. Discr. Algorithms (New Orleans)
45. Abou-Chacra R, Thouless D J and Anderson P W 1973 J. Phys. C: Solid State Phys. 6 1734
46. Semerjian G 2008 J. Stat. Phys. 130 251
47. Montanari A and Semerjian G 2006 J. Stat. Phys. 124 103
48. Pagnani A, Parisi G and Ratieville M 2003 Phys. Rev. E 68 046706
49. Castellani T, Krzakala F and Ricci-Tersenghi F 2005 Eur. Phys. J. B 47 99
50. Montanari A, Parisi G and Ricci-Tersenghi F 2004 J. Phys. A: Math. Gen. 37 2073
51. Montanari A and Ricci-Tersenghi F 2003 Eur. Phys. J. B 33 339
52. Krzakala F and Zdeborov L 2008 Eur. Phys. Lett. 81 57005
53. Seitz S, Alava M and Orponen P 2005 J. Stat. Mech. P06006
54. Alava M, Ardelius J, Aurell E, Kaski P, Krishnamurthy S, Orponen P and Seitz S 2007 Preprint 0711.4902
55. Krzakala F and Kurchan J 2007 Phys. Rev. E 76 021122
56. Maneva E, Mossel E and Wainwright M J 2007 J. Am. Chem. Soc. 54 1
57. Pretti M 2005 J. Stat. Mech. P11008
58. Montanari A, Ricci-Tersenghi F and Semerjian G 2007 Proc. 45th Allerton Conf. on Comm. Control and Computing
59. Ricci-Tersenghi F and Semerjian G 2008 in preparation