Clustering analysis of the ground-state structure of the vertex-cover problem

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

Volumn 70, Issue 6 2, 2004, Pages

  Barthel, Wolfgang ^a   Hartmann, Alexander K ^a  

^a UNIVERSITY OF GÖTTINGEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTER SCIENCE; COMPUTER SIMULATION; CORRELATION METHODS; EIGENVALUES AND EIGENFUNCTIONS; GRAPH THEORY; GROUND STATE; MATRIX ALGEBRA; MONTE CARLO METHODS; POLYNOMIALS; THERMODYNAMICS;

BRANCH-AND-BOUND ALGORITHMS; HIERARCHICAL CLUSTERING; HIERARCHICAL CLUSTERING METHODS; PHASE BOUNDARY;

PROBLEM SOLVING;

EID: 41349113333     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.70.066120     Document Type: Article

References (60)

1. Reviews on spin glasses can be found in K. Binder and A.P. Young, Rev. Mod. Phys. 58, 801 (1986); M. Mézard, G. Parisi, and M.A. Virasoro, Spin Glass Theory and Beyond (World Scientific, Singapore, 1987); K.H. Fisher and J.A. Hertz, Spin Glasses (Cambridge University Press, Cambridge, England, 1991) ; Spin Glasses and Random Fields, edited by A. P. Young (World Scientific, Singapore, 1998).
2. Reviews on spin glasses can be found in K. Binder and A.P. Young, Rev. Mod. Phys. 58, 801 (1986); M. Mézard, G. Parisi, and M.A. Virasoro, Spin Glass Theory and Beyond (World Scientific, Singapore, 1987); K.H. Fisher and J.A. Hertz, Spin Glasses (Cambridge University Press, Cambridge, England, 1991) ; Spin Glasses and Random Fields, edited by A. P. Young (World Scientific, Singapore, 1998).
3. Reviews on spin glasses can be found in K. Binder and A.P. Young, Rev. Mod. Phys. 58, 801 (1986); M. Mézard, G. Parisi, and M.A. Virasoro, Spin Glass Theory and Beyond (World Scientific, Singapore, 1987); K.H. Fisher and J.A. Hertz, Spin Glasses (Cambridge University Press, Cambridge, England, 1991) ; Spin Glasses and Random Fields, edited by A. P. Young (World Scientific, Singapore, 1998).
4. Reviews on spin glasses can be found in K. Binder and A.P. Young, Rev. Mod. Phys. 58, 801 (1986); M. Mézard, G. Parisi, and M.A. Virasoro, Spin Glass Theory and Beyond (World Scientific, Singapore, 1987); K.H. Fisher and J.A. Hertz, Spin Glasses (Cambridge University Press, Cambridge, England, 1991) ; Spin Glasses and Random Fields, edited by A. P. Young (World Scientific, Singapore, 1998).
5. D. Sherrington and S. Kirkpatrick, Phys. Rev. Lett. 35, 1792 (1975).
6. G. Parisi, Phys. Rev. Lett. 43, 1754 (1979); J. Phys. A 13, 1101 (1980); 13, 1887 (1980); 13, L115 (1980); 50, 1946 (1983).
7. G. Parisi, Phys. Rev. Lett. 43, 1754 (1979); J. Phys. A 13, 1101 (1980); 13, 1887 (1980); 13, L115 (1980); 50, 1946 (1983).
8. G. Parisi, Phys. Rev. Lett. 43, 1754 (1979); J. Phys. A 13, 1101 (1980); 13, 1887 (1980); 13, L115 (1980); 50, 1946 (1983).
9. G. Parisi, Phys. Rev. Lett. 43, 1754 (1979); J. Phys. A 13, 1101 (1980); 13, 1887 (1980); 13, L115 (1980); 50, 1946 (1983).
10. G. Parisi, Phys. Rev. Lett. 43, 1754 (1979); J. Phys. A 13, 1101 (1980); 13, 1887 (1980); 13, L115 (1980); 50, 1946 (1983).
11. M. Mézard, G. Parisi, and M.A. Virasoro, Spin Glass Theory and Beyond (Ref. [1]).
12. K.H. Fisher and J.A. Hertz, Spin Glasses (Cambridge University Press, Cambridge, England, 1991).
13. R. Rammal, G. Toulouse, and M.A. Virasoro, Rev. Mod. Phys. 58, 765 (1986).
14. M. Talagrand, C. R. Math. 337, 111 (2003).
15. A.P. Young, Phys. Rev. Lett. 51, 1206 (1983).
16. G. Parisi, F. Ritort, and F. Slanina, J. Phys. A 26, 3775 (1993).
17. A. Billoire, S. Franz, and E. Marinari, J. Phys. A 36, 15 (2003).
18. J. Sinova, G. Canright, and A.H. MacDonald, Phys. Rev. Lett. 85, 2609 (2000).
19. J. Sinova, G. Canright, H.E. Castillo, and A.H. MacDonald, Phys. Rev. B 63, 104427 (2001).
20. G. Hed, A.P. Young, and E. Domany, Phys. Rev. Lett. 92, 157201 (2004).
21. F. Krzakala and O.C. Martin, Phys. Rev. Lett. 85, 3013 (2000).
22. M. Palassini and A.P. Young, Phys. Rev. Lett. 85, 3017 (2000).
23. G. Biroli, R. Monasson, and M. Weigt, Eur. Phys. J. B 14, 551 (2000).
24. M. Mézard, G. Parisi, and R. Zecchina, Science 297, 812 (2002).
25. M. Mézard and R. Zecchina, Phys. Rev. E 66, 056126 (2002).
26. S. Mertens, Phys. Rev. Lett. 81, 4281 (1998).
27. S. Mertens, Phys. Rev. Lett. 84, 1347 (2000).
28. R. Mulet, A. Pagnani, M. Weigt, and R. Zecchina, Phys. Rev. Lett. 89, 268701 (2002).
29. M. Weigt and A.K. Hartmann, Phys. Rev. Lett. 84, 6118 (2000).
30. A.K. Hartmann and M. Weigt, Theor. Comput. Sci. 265, 199 (2001).
31. M. Weigt and A.K. Hartmann, Phys. Rev. E 63, 056127 (2001).
32. H. Zhou, Eur. Phys. J. B 32, 265 (2003).
33. A.K. Hartmann and M. Weigt, J. Phys. A 36, 11069 (2003).
34. M.R. Garey and D.S. Johnson, Computers and Intractability (Freeman, New York, 1979).
35. Frontiers in Problem Solving; Phase Transitions and Complexity, edited by T. Hogg, B.A. Huberman, and C. Williams [Artif. Intell. 81, 1 (1996)].
36. Special issue of Theor. Comput. Sci. 265 (2001), edited by O. Dubois, R. Monasson, B. Selman, and R. Zecchina.
37. R. Monasson and R. Zecchina, Phys. Rev. Lett. 76, 3881 (1996); Phys. Rev. E 56, 1357 (1997).
38. R. Monasson and R. Zecchina, Phys. Rev. Lett. 76, 3881 (1996); Phys. Rev. E 56, 1357 (1997).
39. R. Monasson, R. Zecchina, S. Kirkpatrick, B. Selman, and L. Troyansky, Nature (London) 400, 133 (1999).
40. M. Weigt, in New Optimization Algorithms in Physics, edited by A.K. Hartmann and H. Rieger (Wiley-VCH, New York, 2004).
41. R. Zecchina, in New Optimization Algorithms in Physics (Ref. [32]).
42. M. Mezard, F. Ricci-Tersenghi, and R. Zecchina, J. Stat. Phys. 111, 505 (2003).
43. D. Mitchell, B. Selman, and H. Levesque, in Proceedings of the 10th National Conference Artificial Intelligence (AAAI-92) (AAAI Press/MIT Press, Cambridge, MA, 1992), p. 440.
44. B. Selman and S. Kirkpatrick, Science 264, 1297 (1994).
45. P. Erdös and A. Rényi, Publ. Math., Inst. Hautes Etud. Sci. 5, 17 (1960).
46. B. Bollobas, Random Graphs (Academic, New York, 1985).
47. M. Bauer and O. Golinelli, Phys. Rev. Lett. 86, 2621 (2001).
48. M. Bauer and O. Golinelli, Eur. Phys. J. B 24, 339 (2001).
49. R.E. Tarjan and A.E. Trojanowski, SIAM J. Comput. 6, 537 (1977).
50. E. Marinari and G. Parisi, Europhys. Lett. 19, 451 (1992).
51. K. Hukushima and K. Nemoto, J. Phys. Soc. Jpn. 65, 1604 (1996).
52. D.P. Landau and K. Binder, A Guide to Monte Carlo Simulations in Statistical Physics (Cambridge University Press, Cambridge, England, 2000).
53. E. Marinari, in Advances in Computer Simulation, edited by J. Kertśz and Imre Kondor (Springer-Verlag, Berlin, 1998), p. 50.
54. A.K. Hartmann, Phys. Rev. E 63, 016106 (2001).
55. A.K. Hartmann, J. Phys. A 33, 657 (2000).
56. This is different compared to the application of ballistic search for spin glasses [47]. There it depends also on the order of the spin flips whether a path in configuration space is found or not.
57. A.K. Jain and R.C. Dubes, Algorithms for Clustering Data (Prentice-Hall, Englewood Cliffs, NJ, 1988).
58. G. Hed, A.K. Hartmann, D. Stauffer, and E. Domany, Phys. Rev. Lett. 86, 3148 (2001).
59. S. Ciliberti and E. Marinari, e-print cond-mat/0304273.
60. J. Ward, J. Am. Stat. Assoc. 58, 236 (1963).