Phase Transitions in Combinatorial Optimization Problems: Basics, Algorithms and Statistical Mechanics

Phase Transitions in Combinatorial Optimization Problems: Basics, Algorithms and Statistical Mechanics

Volumn , Issue , 2006, Pages 1-348

  Hartmann, Alexander K ^a   Weigt, Martin ^b  

^a UNIVERSITY OF GÖTTINGEN   (Germany)

^b ISI FOUNDATION   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84889488066     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1002/3527606734     Document Type: Book

References (359)

1. S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, Science 220, 671 (1983).
2. M. Mézard and G. Parisi, J. Physique 47, 1285 (1986).
3. N. J. Cerf, J. Boutet de Monvel, O. Bohigas, O. C. Martin, and A. G. Percus, Journal de Physique I 7, 117 (1997).
4. A. G. Percus and O. C. Martin, J. Stat. Phys. 94, 739 (1999).
5. A. Chakraborti and B. K. Chakrabarti, Eur. Phys. J. B 16, 677 (2000).
6. D. S. Dean, D. Lancaster, and S. N. Majumdar, arXiv preprint cond-mat/0411111.
7. M. Mézard, G. Parisi, and M. A. Virasoro, Spin Glass Theory and Beyond (World Scientific, Singapore, 1987).
8. K. H. Fisher and J. A. Hertz, Spin Glasses (Cambridge University Press, 1991).
9. I. P. Gent and T. Walsh, Artif. Intell. 88, 349 (1996).
10. A. V. Aho, J. E. Hopcroft, and J. D. Ullman, The Design and Analysis of Computer Algorithms, (Addison-Wesley, Reading (MA) 1974)
11. R. Sedgewick, Algorithms in C, (Addison-Wesley, Reading (MA) 1990).
12. T. H. Cormen, S. Clifford, C. E. Leiserson, and R. L. Rivest, Introduction to Algorithms, (MIT Press, 2001).
13. L. Euler, Commentarii Academiae Scientiarum Imperialis Petropolitanae 8, 128 (1736).
14. E. L. Lawler, Combinatorial Optimization: Networks and Matroids, (Holt, Rinehard and Winston, New York 1976).
15. K. Appel andW. Haken, Discrete Math. 16, 179 (1976).
16. R. L. Graham, M. Grötschel, and L. Lovász, Handbook of Combinatorics, (Elsevier Science Publishers, Amsterdam 1995).
17. L. Lovász and M. D. Plummer, Matching Theory, (Elsevier Science Publishers, Amsterdam 1986).
18. H. Rieger, Ground state properties of frustrated systems, in: J. Kertesz and I. Kondor (eds.), Advances in Computer Simulation, Lecture Notes in Physics 501, (Springer, Heidelberg, 1998).
19. M. Alava, P. Duxbury, C. Moukarzel, and H. Rieger, Combinatorial optimization and disordered systems, in: C. Domb and J. L. Lebowitz (eds.), Phase Transitions and Critical Phenomena, 18, 141 (Academic Press, Cambridge 2000).
20. A. K. Hartmann and H. Rieger, Optimization Algorithms in Physics, (Wiley-VCH, Berlin, 2001).
21. W. J. Cook, W. H. Cunningham, W. R. Pulleyblank, and A. Schrijver, Combinatorial Optimization, (JohnWiley & Sons, New York 1998).
22. B. Korte and J. Vygen, CombinatorialOptimization -Theory and Algorithms, (Springer, Heidelberg 2000).
23. A. V. Aho, J. E. Hopcroft, and J. D. Ullman, The Design and Analysis of Computer Algorithms, (Addison-Wesley, Reading (MA) 1974).
24. R. Sedgewick, Algorithms in C, (Addison-Wesley, Reading (MA) 1990).
25. T. H. Cormen, S. Clifford, C. E. Leiserson, and R. L. Rivest, Introduction to Algorithms, (MIT Press, Cambridge (USA) 2001).
26. P. Erdos and A. Rényi, Magyar Tud. Akad. Mat. Kutat Int. Kozl. 5, 17 (1960).
27. B. Bollobás, Random Graphs, (Academic Press, New York 1985).
28. D. Stauffer and A. Aharony, Introduction to Percolation Theory, (Taylor & Francis, London 1994).
29. B. Pittel, J. Spencer, and N. C. Wormald, J. Comb. Theory B 67, 111 (1996).
30. N. C. Wormald, Ann. Appl. Prob. 5, 1217 (1995).
31. A. M. Turing, Proc. London Math. Soc. 42, 230; 43 544 (1936).
32. C. H. Papadimitriou, Computational Complexity (Addison-Wesley, 1994).
33. M. Presburger, Comptes Rendus du I congrés de Mathèmaticiens des Pays Slaves, 92-101 (1929). [Mojezesz Presburger, born 1904, died probably 1943 in the Warschauer Getto].
34. M. J. Fischer, M. O. Rabin, Proceedings of the SIAM-AMS Symposium in Applied Mathematics 7, 27 (1974).
35. Wikipedia, the free encyclopedia, see http://www.wikipedia.org/wiki/Presburger_arithmetic
36. S. A. Cook, Ann. ACM Symp. on Theory of Computing, 151 (Assoc. for Comp. Mach., New York 1971).
37. I. Wegener, Theoretische Informatik -eine algorithmenorientierte Einführung, (Teubner, Stuttart, Leipzig 1999).
38. R. E. Ladner, J. Assoc. Comput. Mach. 22, 155 (1975).
39. M. R. Garey and D. S. Johnson, Computer and Intractability: A Guide to the Theory of NP-Completeness, (W. H. Freeman & Company, San Francisco 1979).
40. D. Chandler, Introduction to Modern Statistical Mechanics, (Oxford University Press, Oxford 1987).
41. J. M. Yeomans, Statistical Mechanics of Phase Transitions, (Larendon Press, Oxford 1992).
42. L. E. Reichl, A Modern Course in Statistical Physics, (John Wiley & sons, New York 1998).
43. E. Ising, Z. Phys. 31, 253 (1925).
44. L. Onsager, Phys. Rev. 65, 177 (1944).
45. M. Mézard, G. Parisi, M. A. Virasoro, Spin Glasses and Beyond, (World Scientific, Singapore 1987).
46. S. F. Edwards and P. W. Anderson, J. Phys. 5, 965 (1975).
47. D. Sherrington and S. Kirkpatrick, Phys. Rev. Lett. 35, 1792 (1975).
48. G. Parisi, J. Phys. A 13, 1101 (1980).
49. M. Talagrand, To app. in Ann. Math. The result was first announced in C. R. A. S. 337, 111 (2003).
50. I. Kanter and H. Sompolinsky, Phys. Rev. Lett. 58, 164 (1987).
51. Viana and A. Bray, J. Phys. C 18, 3037 (1985).
52. C. de Dominicis and P. Mottishaw, J. Phys. A 20, L1267 (1987).
53. P. Mottishaw and C. de Dominicis, J. Phys. A 20, L375 (1987).
54. K. Y. M. Wong and D. Sherrington, J. Phys. A 21, L459 (1988).
55. Y. Goldschmidt and P. Y. Lai, J. Phys. A 23, L775 (1990).
56. R. Monasson, J. Phys. A 31, 513 (1998).
57. M. Mézard and G. Parisi, Eur. Phys. J. B 20, 217 (2001).
58. S. Franz and M. Leone, J. Stat. Phys. 111, 535 (2003).
59. H. Bethe, Proc. Roy. Soc. Lond. 150, 552 (1935).
60. R. Peierls, Proc. Roy. Soc. Lond. 154, 207 (1936).
61. K. Mehlhorn and St. Näher, The LEDA Platform of Combinatorial and Geometric Computing (Cambridge University Press, Cambridge 1999); see also http://www.mpi-sb.mpg.de/LEDA/leda.html
62. J. Siek, L.-Q. Lee, A. Lumsdainesee, The Boost Graph Library, (Addison-Wesley, Reading (MA) 2001); see also http://www.boost.org/libs/graph/doc/index.html
63. J. Hromkovic, Algorithms for Hard Problems, (Springer, Heidelberg, 2001).
64. E. L. Lawler and D. E. Wood, Oper. Res. 14, 699 (1966).
65. R. Lüling and B. Monien, in: Sixth International Parallel Processing Symposium, (IEEE Comput. Soc. Press, Los Alamitos, USA 1992).
66. M. Shindo and E. Tomita, Syst. Comp. Jpn. 21, 1 (1990).
67. A. K. Hartmann, W. Barthel and M. Weigt, submitted to Comp. Phys. Comm.
68. M. N. Barber, in: C. Domb and J. L. Lebowitz, Phase Transitions and Critical Phenomena 8, 146, (Academic Press, London 1983).
69. V. Privman (ed.), Finite Size Scaling and Numerical Simulation of Statistical Systems, (World Scientific, Singapore, 1990).
70. J. Cardy, Scaling and Renormalization in Statistical Physics, (Cambridge University Press, Cambridge 1996).
71. P. G. Gazmuri, Networks 14, 367 (1984).
72. A. M. Frieze, Discr. Math. 81, 171 (1990).
73. M. Weigt and A. K. Hartmann, Phys. Rev. Lett. 84, 6118 (2000).
74. M. Bauer and O. Golinelli, Eur. Phys. J. B 24, 339 (2001).
75. R. E. Tarjan and A. E. Trojanowski, SIAM J. Comp. 6, 537 (1977).
76. M. E. J. Newman und G. T. Barkema, Monte Carlo Methods in Statistical Physics (Clarendon Press, Oxford, 1999).
77. D. P. Landau and K. Binder, A Guide to Monte Carlo Simulations in Statistical Physics, (Cambridge University Press, Cambridge 2000).
78. L. E. Reichl, A modern Course in Statistical Physics, (Wiley, New York 1998).
79. M. Weigt and A. K. Hartmann, Europhys. Lett. 62, 533 (2003).
80. E. Marinari and G. Parisi, Europhys. Lett. 19, 451 (1992).
81. K. Hukushima and K. Nemoto, J. Phys. Soc. Jpn. 65, 1604 (1996).
82. W. Barthel and A. K. Hartmann, To appear in Phys. Rev. B (2004), preprint condmat/0403193.
83. A. K. Hartmann and M. Weigt, J. Theor. Comp. Sci. 265, 199 (2001).
84. M. Weigt and A. K. Hartmann, Phys. Rev. E 63, 056127 (2001).
85. M. Weigt and A. K. Hartmann, Phys. Rev. Lett. 86, 1658 (2001).
86. Reviews on spin glasses can be found in: K. Binder and A. P. Young, Rev. Mod. Phys. 58, 801 (1986)
87. M. Mézard, G. Parisi, M. A. Virasoro, Spin Glass Theory and Beyond, (World Scientific, Singapore 1987).
88. D. Sherrington and S. Kirkpatrick, Phys. Rev. Lett. 35, 1792 (1975).
89. G. Parisi, Phys. Rev. Lett. 43, 1754 (1979)
90. K. H. Fisher and J. A. Hertz, Spin Glasses, (Cambridge University Press, Cambridge 1991).
91. R. Rammal, G. Toulouse, and M. A. Virasoro, Rev. Mod. Phys. 58, 765 (1986).
92. M. Talagrand, C. R. A. S. 337, 111 (2003).
93. A. P. Young, Phys. Rev. Lett. 51, 13 (1983).
94. G. Parisi, F. Ritort and F. Slanina, J. Phys. A 26, 3775 (1993).
95. A. Billoire, S. Franz, and E. Marinari, J. Phys. A 36 (2003).
96. J. Sinova, G. Canright, and A. H. MacDonald, Phys. Rev. Lett. 85, 2609 (2000).
97. J. Sinova, G. Canright, H. E. Castillo, and A. H. MacDonald, Phys. Rev. B 63, 104427 (2001).
98. G. Hed, A. P. Young, and E. Domany, Phys. Rev. Lett. 92, 157201 (2004).
99. F. Krzakala and O. C. Martin, Phys. Rev. Lett. 85, 3013 (2000).
100. M. Palassini and A. P. Young, Phys Rev. Lett. 85, 3017 (2000).
101. R. Monasson and R. Zecchina, Phys. Rev. Lett. 76, 3881 (1996); Phys. Rev. E 56, 1357 (1997).
102. R. Monasson, R. Zecchina, S. Kirkpatrick, B. Selman, and L. Troyansky, Nature 400, 133 (1999).
103. G. Biroli, R. Monasson, and M. Weigt, Eur. Phys. J. B 14, 551 (2000).
104. M. Mézard, G. Parisi, and R. Zecchina, Science 297, 812 (2002).
105. M. Mézard and R. Zecchina, Phys. Rev. E 66, 056126 (2002).
106. M. Weigt, in: A. K. Hartmann and H. Rieger (eds.), New Optimization Algorithms in Physics, 121, (Wiley-VCH, Weinheim 2004).
107. R. Zecchina, in: A. K. Hartmann and H. Rieger (eds.), New Optimization Algorithms in Physics, 183, (Wiley-VCH, Weinheim 2004).
108. A. K. Hartmann, J. Phys. A 33, 657 (2000).
109. M. Weigt and A. K. Hartmann, Phys. Rev. Lett 84, 6118 (2000).
110. M. Weigt and A. K. Hartmann, Phys. Rev. E 63, 056127 (2001).
111. M. Mézard and G. Parisi, J. Phys. Lett. 46, L771 (1985).
112. Y. Fu and P. W. Anderson, J. Phys. A 19, 1605 (1986).
113. M. Mézard and G. Parisi, J. Physique 47, 1285 (1986).
114. D. Mitchell, B. Selman, and H. Levesque, in: Proc. of the 10th Natl. Conf. on Artificial Intelligence AAAI-92, 459 (1992).
115. B. Selman and S. Kirkpatrick, Science (Washington DC) 264, 1297 (1994).
116. R. Monasson and R. Zecchina, Phys. Rev. Lett. 76, 3881 (1996); Phys. Rev E56, 1357 (1997).
117. T. Hogg, B. A. Huberman, and C. Williams (eds.), Special issue of Artif. Intell. 81 (1996).
118. O. Dubois, R. Monasson, B. Selman, and R. Zecchina (eds.), Special issue of Theor. Comp. Sci. 265 (2001).
119. E. Marinari, H. Nishimori, and F. Ricci-Tersenghi (eds.), Special issue of J. Phys. A 36, nr. 43 (2003).
120. A. M. Frieze, Discr. Math. 81, 171 (1990).
121. H. Zhou, Eur. Phys. J. B 32, 265 (2003).
122. S. Kirckpatrick, C. D. Gelatt, and M. P. Vecchi, Science 220, 671 (1983).
123. B. Selman, H. Kautz, and B. Cohen, in Cliques, Coloring and Satisfiability, ed. by D. S. Johnson and M. A. Trick, DIMACS series vol. 26 (AMS, Providence 1996).
124. M. Weigt and A. K. Hartmann, Phys. Rev. Lett. 86, 1658 (2001).
125. S. Cocco and R. Monasson, Phys. Rev. Lett. 86, 1654 (2001).
126. S. Cocco and R. Monasson, Eur. Phys. J. B 22, 505 (2001)
127. P. G. Gazmuri, Networks 14, 367 (1984)
128. M. Bauer and O. Golinelli, Phys. Rev. Lett. 86, 2621 (2001)
129. C. P. Gomes, B. Selman, N. Crato, and H. Kautz, J. Automated Reasoning 24, 67 (2000)
130. C. P. Gomes, B. Selman, and H. Kautz, Proc. AAAI-98, 431 (Madison, WI, 1998).
131. A. Montanari and R. Zecchina, Phys. Rev. Lett. 88, 178701 (2002).
132. S. Cocco and R. Monasson, Phys. Rev. E 66, 037101 (2002).
133. B. J. Frey, Graphical Models for Machine Learning and Digital Communication (MIT Press, 1998).
134. F. R. Kschischang, B. R. Frey, and H. A, Loeliger, IEEE Trans. Info. Theory 47, 498 (2001).
135. J. S. Yedidia, W. T. Freeman, and Y. Weiss, Technical report TR-2001-22 of the Mitsubishi Electric Research Laboratories (2002).
136. M. Mézard and G. Parisi, Eur. Phys. J. B 20, 217 (2001).
137. M. Mézard, G. Parisi, and R. Zecchina, Science 297, 812 (2002).
138. M. Mézard and R. Zecchina, Phys. Rev. E 66, 056126 (2002).
139. A. Braunstein, M. Mézard, and R. Zecchina, submitted to Rand. Struct. Alg.; arXiv preprint cs. CC/0212002.
140. A. Braunstein, R. Mulet, A. Pagnani, M. Weigt, and R. Zecchina, Phys. Rev. E 68, 036702 (2003).
141. A. Braunstein, M. Mézard, M. Weigt, and R. Zecchina, To appear in Computational Complexity and Statistical Physics, Editors: A. Percus, G. Istrate and C. Moore (2005).
142. M. Weigt and A. K. Hartmann, Phys. Rev. E 63, 056127 (2001).
143. H. Zhou, Eur. Phys. J. B 32, 265 (2003).
144. D. Mitchell, B. Selman, and H. Levesque, in: Proc. of the 10th Natl. Conf. on Artificial Intelligence AAAI-92, 459 (1992).
145. B. Selman and S. Kirkpatrick, Science (Washington DC) 264, 1297 (1994).
146. R. Monasson and R. Zecchina, Phys. Rev. Lett. 76, 3881 (1996).
147. R. Monasson and R. Zecchina, Phys. Rev. E 56, 1357 (1997).
148. R. Monasson, R. Zecchina, S. Kirkpatrick, B. Selman, and L. Troyansky, Nature 400, 133 (1999).
149. M. Mézard, G. Parisi, and R. Zecchina, Science 297, 812 (2002).
150. M. Mézard and R. Zecchina, Phys. Rev. E 66, 056126 (2002).
151. M. Mézard and G. Parisi, Eur. Phys. J. B 20, 217 (2001).
152. J. Gu, P. W. Purdom, J. Franco, and B. W. Wah, in: D. Du, J. Gu, and P. Pardalos (eds), DIMACS Series in Discrete Mathematics and Theoretical Computer Science 35, 19 (American Mathematical Society, Providence 1997).
153. B. Aspvall, M. F. Plass, and R. E. Tarjan, Inf. Proc. Lett. 8, 121 (1979).
154. A. V. Aho, J. E. Hopcroft, and J. D. Ullman, The Design and Analysis of Computer Algorithms, (Addison-Wesley, Reading (MA) 1974).
155. E. M. Reingold, J. Nievergelt, and N. Deo, Combinatorial Algorithms -Theory and Practice, (Prentice-Hall, Englewood Cliffs (NJ) 1977).
156. M. Davis and H. Putnam, J. Assoc. Comp. Machin. 7, 201 (1960).
157. M. Davis, G. Logemann, and D. Loveland, Commun. ACM 5, 394 (1962).
158. I. Lynce and J. P. Marques-Silva, Ann. Math. Artif. Intell. 37, 307 (2003).
159. R. M. Stallman and G. J. Sussman, Artif. Intell. 9, 135 (1977).
160. R. Dechter, Artif. Intell. 41, 273 (1989/1990).
161. B. Monien and E. Speckenmeyer, Discr. Appl. Math. 10, 287 (1985).
162. R. Rodosek, in: J. Calmet, J. A. Campbell, and J. Pfalzgraf (eds.), Proc. 3rd Intern. Conf. on AI and Symbolic Math. Computation, Lecture Notes on Computer Science 1138, 197 (Springer, Heidelberg 1996).
163. E. Dantsin, A. Goerdt, E. A. Hirsch, and U. Schöning, in: U. Montanari et al. (eds.), Proc. Int. Colloq. on Automata, Languages and Programming ICALP'00, Lecture Notes in Computer Science 1853, 236 (Springer, Heidelberg 2000).
164. E. Dantsin et al., Theor. Comp. Sci. 289, 69 (2002).
165. T. Stützle, H. Hoos, and Andrea Roli, Technical Report AIDA-01-02, Darmstadt University of Technology, Computer Science Department, Intellectics Group (2001).
166. C. H. Papadimitriou, in: Proc. 32nd Ann. IEEE Symp. on Found. of Comp. Sci. FOCS'91, 163 (1991).
167. L. E. Reichl, A Modern Course in Statistical Physics, (John Wiley & sons, New York 1998).
168. B. Selman, H. Kautz, and B. Cohen, in: D. S. Johnson and M. A. Trick (eds.), Cliques, Coloring and Satisfiability, DIMACS Series in Discrete Mathematics and Theoretical Computer Science vol. 26, 337 (American Mathematical Society, Providence 1996).
169. U. Schöning, in: Proc. 40th Ann. IEEE Symp. on Found. of Comp. Sci. FOCS'99, 410 (IEEE, New York 1999).
170. U. Schöning, Algorithmica 32, 615 (2002).
171. W. Feller, An Inroduction to Probability Theory and its Applications, (Wiley, New York 1968).
172. G. R. Grimmet and D. R. Stirzaker, Probability and Random Processes, (Oxford University Press, Oxford 1992).
173. R. Schuler, U. Schöning, and O. Watanabe, Res. Rep. Math. Comp. Sci. Ser. C 146, 1 (2001).
174. T. Hofmeister, U. Schöning, R. Schuler, and O. Watanabe, in: H. Alt and A. Ferreira (eds.), Proc. 19th Ann. Symp. Theoretical Aspects Computer Science STACS 2002, 192 (Spinger, Berlin 2002).
175. S. Baumer and R. Schuler, in: E. Giunchiglia and A. Tacchella (eds.), Theory and Applications of Satisfiability Testing. 6th Intl. Conf. SAT 2003, 150 (Springer, Berlin 2004).
176. E. Friedgut, J. Amer. Math. Soc. 12, 1017 (1999).
177. O. Dubois and Y. Boufkhad, J. Algorithms 24, 395 (1997).
178. L. M. Kirousis, E. Kranakis, and D. Krizanc, Rand. Struct. Alg. 12, 253 (1998).
179. Y. Boufkhad, O. Dubois, and J. Mandler, Electr. Coll. Comput. Compl. 10, 07 (2003).
180. M. T. Chao and J. Franco, SIAM Journal on Computing 15, 1106 (1986); Information Science 51, 289 (1990).
181. D. Achlioptas, Theor. Comp. Sci. 265, 159 (2001).
182. J. Franco, Theor. Comp. Sci. 265, 147 (2001).
183. A. C. Kaporis, L. M. Kirousis, and E. G. Lalas, in: R. H. Möhring and R. Ramam (eds.), Algorithms -ESA 2002, Proceedings" (Springer, New York 2002).
184. D. Achlioptas and Y. Peres, Journal of the AMS 17, 947 (2004).
185. G. Biroli, M. Weigt, and R. Monasson, Eur. Phys. J. B 14, 551 (2000).
186. S. Mertens, M. Mézard, and R. Zecchina, arXiv preprint cs. CC/0309020.
187. A. Montanari, G. Parisi, and F. Ricci-Tersenghi, J. Phys. A 37, 2073 (2004).
188. Alekhnovich, Ben-Sasson, proc. FOCS'02, 352 (2003); Electr. Coll. Comput. Compl. 11, 16 (2004).
189. W. Barthel, A. K. Hartmann, and M. Weigt, Phys. Rev. E 67, 066104 (2003).
190. G. Semerjian and R. Monasson, Phys. Rev. E 67, 066103 (2003).
191. S. Kirckpatrick, C. D. Gelatt, and M. P. Vecchi, Science 4598, 671 (1983).
192. A. K. Hartmann and H. Rieger, Optimization Algorithms in Physics, (Wiley-VCH, Berlin, 2001).
193. A. K. Hartmann and H. Rieger, New Optimization Algorithms in Physics, (Wiley-VCH, Berlin, 2004).
194. H. Rieger, Ground state properties of frustrated systems, in: J. Kertesz and I. Kondor (eds.), Advances in Computer Simulation, Lecture Notes in Physics 501, (Springer, Heidelberg, 1998).
195. M. Alava, P. Duxbury, C. Moukarzel, and H. Rieger, Combinatorial optimization and disordered systems, in: C. Domb and J. L. Lebowitz (eds.), Phase Transition and Critical Phenomena, 18, 141 (Academic Press, Cambridge 2000).
196. M. E. J. Newman and G. T. Barkema, Monte Carlo Methods in Statistical Physics (Clarendon Press, Oxford, 1999).
197. D. P. Landau and K. Binder, A Guide to Monte Carlo Simulations in Statistical Physics, (Cambridge University Press, Cambridge 2000).
198. P. J. M. Van Laarhoven and E. H. L. Aarts, Simulated Annealing: Theory and Applications (Mathematics and Its Applications), (Kluwer Academic Publishers, Dordrecht 1987).
199. R. V. V. Vidal, Applied Simulated Annealing (Lecture Notes in Economics and Mathematical Systems 396), (Springer, Heidelberg 1993).
200. E. Marinari and G. Parisi, Europhys. Lett. 19, 451 (1992).
201. K. Hukushima and K. Nemoto, J. Phys. Soc. Jpn. 65, 1604 (1996).
202. U. Wolff, Phys. Rev. Lett. 62, 361 (1989).
203. H. G. Evertz, Adv. Phys. 52, 1 (2003).
204. C. Dress and W. Krauth, J. Phys. A 28, L597 (1995).
205. W. Krauth, in: A. K. Hartmann and H. Rieger (eds.), New Optimization Algorithms in Physics, 7 (Wiley-VCH, Berlin, 2004).
206. N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, J. Chem. Phys. 21, 1087 (1953).
207. M. E. J. Newmann and G. T. Barkema, Phys. Rev. E 53, 393 (1996).
208. D. A. Kessler and M. Bretz, Phys. Rev. B 41, 4778 (1990).
209. S. Liang, Phys. Rev. Lett. 69, 2145 (1992).
210. L. Santen and W. Krauth, Nature 405, 550 (2000).
211. M. N. Rosenbluth and A. W. Rosenbluth, J. Chem. Phys. 23, 356 (1955).
212. F. Wang and D. P. Landau, Phys. Rev. Lett. 86, 2050 (2001).
213. G. M. Torrie and J. P. Valleau, J. Comp. Phys. 23, 187 (1977).
214. B. Berg and T. Neuhaus, Phys. Lett. B 267, 249 (1991);
215. Phys. Rev. Lett. 68, 9 (1992).
216. S. Alder, S. Trebst, A. K. Hartmann, and M. Troyer, J. Stat. Mech. P07008 (2004).
217. P. Grassberger and H. Frauenkron, in: P. Grassberger, G. T. Barkema, and W. Nadler. (eds.), Workshop on Monte Carlo Approach to Biopolymers and Protein Folding, (World Scientific, Singapure 1998).
218. K. A. Dill, Biochemistry 24, 1501 (1985).
219. K. F. Lau and K. A. Dill, Macromolecules 22, 3986 (1989)
220. H. Frauenkron, U. Bastolla, E. Gerstner, P. Grassberger, andW. Nadler, Phys. Rev. Lett. 80 3149 (1998).
221. U. Bastolla, H. Frauenkron, E. Gerstner, P. Grassberger, and W. Nadler, Proteins: Struct., Fnct., Gen. 32, 52 (1998).
222. G. Zaránd, F. Pázmándi, K. F. Pál, and G. T. Zimányi, Phys. Rev. Lett. 89, 150201 (2002).
223. K. F. Pál, in: A. K. Hartmann and H. Rieger (eds.), New Optimization Algorithms in Physics, 205 (Wiley-VCH, Berlin, 2004).
224. K. F. Pál, Physica A 233, 60 (1996).
225. M. J. Alava et al., submitted to Phys. Rev. B, preprint cond-mat/0407297 (2004).
226. K. F. Pál, Physica A 223, 283 (1996).
227. J. Houdayer and O. C. Martin, Phys. Rev. Lett. 83, 1030 (1999).
228. J. Houdayer and O. C. Martin, Phys. Rev. E 64, 056704 (2001).
229. M. Mitchell, An Introduction to Genetic Algorithms, (MIT Press, Cambridge (USA) 1996).
230. Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs, (Springer, Heidelberg 1994).
231. P. Sutton and S. Boyden, Am. J. Phys. 62, 549 (1994).
232. J. H. Holland, Adaption in Natural and Artificial Systems, (University of Michigan Press, Ann Arbor 1975).
233. A. Yamaguchi and A. Sugamoto, Nucl. Phys. B Proc. Suppl. 83-84, 837 (2000).
234. I. Grigorenko and M. E. Garcia, Physica A 284, 131 (2000).
235. I. Grigorenko and M. E. Garcia, Physica A 291, 439 (2001).
236. A. Ulyanenkov, K. Omote, and J. Harada, Physica B. 283, 237 (2000).
237. T. X. Li, S. Y. Yin, Y. L. Ji, B. L. Wang, C. H. Wang, and J. J. Zhao, Phys. Lett. A 267, 403 (2000).
238. M. Iwamatsu, J. Chem. Phys. 112, 10976 (2000).
239. D. Romero, C. Barron, and S. Gomez, Comp. Phys. Comm. 123, 87 (1999).
240. Cheng Cheng, J. Phys. D 33, 1169 (2000).
241. R. S. Judson and H. Rabitz, Phys. Rev. Lett. 68, 1500 (1992).
242. F. G. Omenetto, B. P. Luce, and A. J. Taylor, J. Opt. Soc. Am. B 16, 2005 (1999).
243. D. G. Ireland, J. Phys. G 26, 157 (2000).
244. B. Ahrens, Meteor. Atmos. Phys. 70, 227 (1999).
245. H. Sadeghi, S. Suzuki, and H. Takenaka, Phys. Earth Plan. Inter. 113, 355 (1999).
246. M. Wahde, Astron. Astroph. Supplement Series 132, 417 (1998).
247. Genetic and Evolutionary Algorithm Toolbox, can be tested three weeks for free, see http://www.geatbx.com/index.html
248. Matlab 5.3.1 is a commercial program for data analysis, numerical computations, plotting and simulation, see http://www.mathworks.com/
249. S. M. Brown, Bioinformatics, (Eaton Publishing, Natick (MA) 2000).
250. R. Durbin, S. Eddy, A. Krogh, and G. Mitchison, Biological Sequence Analysis, (Cambridge University Press, Cambridge 1998).
251. A. K. Hartmann, in: A. K. Hartmann and H. Rieger (eds.), New Optimization Algorithms in Physics, 253 (Wiley-VCH, Berlin, 2004).
252. T. Halpin-Healy and Y.-C. Zhang, Phys. Rep. 254, 215 (1995)
253. M. Kardar and Y.-C. Zhang, Phys. Rev. Lett. 58, 2087 (1987)
254. M. Kardar, Phys. Rev. Lett. 55, 2235 (1985)
255. L. E. Reichl, A Modern Course in Statistical Physics, (John Wiley & sons, New York 1998).
256. A. V. Aho, J. E. Hopcroft, and J. D. Ullman, The Design and Analysis of Computer Algorithms, (Addison-Wesley, Reading (MA) 1974).
257. R. Sedgewick, Algorithms in C, (Addison-Wesley, Reading (MA) 1990).
258. T. H. Cormen, S. Clifford, C. E. Leiserson, andR. L. Rivest, Introduction to Algorithms, (MIT Press, Cambridge (USA) 2001).
259. Y. Imry and S.-K. Ma, Phys. Rev. Lett. 35, 1399 (1975).
260. D. P. Belanger and A. P. Young, J. Magn. and Magn. Mat. 100, 272 (1991).
261. H. Rieger, in: D. Stauffer (ed.): Annual Reviews of Computational Physics II, 295, (World Scientific, Singapore 1995).
262. A. P. Young (ed.), SpinGlasses and Random Fields, (World Scientific, Singapore 1998).
263. K. Binder and A. P. Young, Rev. Mod. Phys. 58, 801 (1986).
264. M. Mezard, G. Parisi, and M. A. Virasoro, Spin Glass Theory and Beyond, (World Scientific, Singapore 1987).
265. K. H. Fisher and J. A. Hertz, Spin Glasses, (Cambridge University Press, Cambridge 1991).
266. J. A. Mydosh, Spin Glasses: an Experimental Introduction, (Taylor and Francis, London 1993).
267. S. Fishman and A. Aharony, J. Phys. C 12, L729 (1979).
268. J. L. Cardy, Phys. Rev. B 29, 505 (1984).
269. D. P. Belanger, A. R. King, V. Jaccarino and J. L. Cardy, Phys. Rev. B 28, 2522 (1983).
270. D. P. Belanger and Z. Slanic, J. Magn. and Magn. Mat. 186, 65 (1998).
271. D. P. Belanger, in Spin Glasses and Random Fields, A. P. Young (Ed.), 251 (World Scientific, 1998).
272. U. Nowak and K. D. Usadel, Phys. Rev. B 39, 2516 (1989).
273. U. Nowak and K. D. Usadel, Phys. Rev. B 44, 7426 (1991).
274. K. D. Usadel and U. Nowak, JMMM 104-107, 179 (1992).
275. T. Nattermann, in Spin Glasses and Random Fields, A. P. Young (Ed.), 277 (World Scientific, 1998).
276. A. Aharony, Phys. Rev B 18, 3318 (1978).
277. M. Aizenman and J. Wehr, Phys. Rev. Lett. 62, 2503 (1989).
278. J. Bricomont and A. Kupiainen, Phys. Rev. Lett. 59, 1829 (1987).
279. T. Schneider and E. Pytte, Phys. Rev. B 15, 1519 (1977).
280. H. Rieger, Phys. Rev B 52, 6659 (1995).
281. M. E. J. Newman and G. T. Barkema, Phys. Rev. B 53, 393 (1996).
282. A. J. Bray and M. A. Moore, J. Phys. C 18 L927 (1985).
283. D. S. Fisher, Phys. Rev. Lett. 56, 416 (1986).
284. J.-C. Picard and H. D. Ratliff, Networks 5, 357 (1975).
285. A. T. Ogielski, Phys. Rev. Lett. 57, 1251 (1986).
286. J. C. Anglès d'Auriac, M. Preissmann and A. Seb, J. Math. and Comp. Model. 26, 1 (1997).
287. J.-C. Picard and M. Queyranne, Math. Prog. Study 13, 8 (1980).
288. A. K. Hartmann and K. D. Usadel, Physica A 214, 141 (1995).
289. A. K. Hartmann, Physica A 248, 1 (1998).
290. S. Bastea and P. M. Duxbury, Phys. Rev. E 58, 4261 (1998).
291. E. T. Seppälä, M. J. Alava, and P. M. Duxbury, Phys. Rev. E 63, 036126 (2001).
292. E. T. Seppälä and M. J. Alava, Phys. Rev. Lett. 84, 3982 (2000).
293. E. T. Seppälä, V. I. Raisanen, and M. J. Alava, Phys. Rev. E 61, 6312 (2000).
294. L. R. Ford and D. R. Fulkerson, Canadian J. Math. 8, 399 (1956).
295. J. D. Claiborne, Mathematical Preliminaries for Computer Networking, (JohnWiley & Sons, New York 1990).
296. W. Knödel, Graphentheoretische Methoden und ihre Anwendung, (Springer, Berlin 1969).
297. M. N. S. Swamy and K. Thulasiraman, Graphs, Networks and Algorithms, (JohnWiley & Sons, New York 1991).
298. L. R. Ford and D. R. Fulkerson, Flows in Networks, (Princeton University Press, Princeton 1962).
299. J. Edmonds and R. M. Karp, J. ACM 19, 248 (1972).
300. E. A. Dinic, Soviet Math. Dokl. 11, 1277 (1970).
301. R. E. Tarjan, Data Structures and Network Algorithms, (Society for Industrial and Applied Mathematics, Philadelphia 1983).
302. A. V. Goldberg and R. E. Tarjan, J. ACM 35, 921 (1988).
303. B. Cherkassky and A. Goldberg, Algorithmica 19, 390 (1997).
304. A. V. Goldberg and R. Satish, J. ACM 45, 783 (1998).
305. K. Mehlhorn and S. Näher, The LEDA Platform of Combinatorial and Geometric Computing (Cambridge University Press, Cambridge 1999); see also http://www.algorithmic-solutions.de
306. J. Siek, L.-Q. Lee, A. Lumsdainesee, The Boost Graph Library, (Addison-Wesley, Reading (MA) 2001); see also http://www.boost.org/libs/graph/doc/index.html
307. A. A. Middleton, Phys. Rev. Lett. 88, 017202 (2002).
308. A. K. Hartmann and U. Nowak, Eur. Phys. J. B 7, 105 (1999).
309. J.-C. Anglès d'Auriac and N. Sourlas, Europhys. Lett. 39, 473 (1997).
310. M. R. Swift, A. J. Bray, A. Maritan, M. Cieplak, and J. R. Banavar, Europhys. Lett. 38, 273 (1997).
311. N. Sourlas, Comp. Phys. Comm. 121-122, 183 (1999).
312. A. A. Middleton and D. S. Fisher, Phys. Rev. B 65, 134411 (2002).
313. A. K. Hartmann and A. P. Young, Phys. Rev. B 64, 214419 (2001).
314. R. B. Potts, Proc. Camb. Phil. Soc. 48, 106 (1952).
315. F. Y. Wu, Rev. Mod. Phys. 54, 235 (1982).
316. R. J. Baxter, J. Phys. C 6, L445 (1973).
317. C. M. Fortuin and P. W. Kasteleyn, Physica 57, 536 (1972).
318. R. Juhász, H. Rieger, and F. Iglói, Phys. Rev. E 64, 056122 (2001).
319. A. Schrijver, Combinatorial Optimization -Polyhedra and Efficiency Volume B, (Springer, Berlin 2003).
320. M. Grötschel, L. Lovász, A. Schrijver, Combinatorica 1, 169 (1981).
321. A. Schrijver, Journal of Combinatorial Theory Ser. B 80, 346 (2000).
322. S. Iwata, L. Fleischer, and S. Fujishige, Journal of the ACM 48, 761 (2001).
323. J.-Ch. Anglès d'Auriac, F. Iglói, M. Preissmann, and A. Sebo, J. Phys. A 35, 6973 (2002).
324. J.-Ch. Anglès d'Auriac, in: A. K. Hartmann and H. Rieger, New Optimization Algorithms in Physics, 101 (Wiley-VCH, Berlin, 2004).
325. F. Barahona, J. Phys. A 15, 3241 (1982).
326. S. F. Edwards and P. W. Anderson, J. de Phys. 5, 965 (1975).
327. B. Müller and J. Reinhardt, Neural Networks -An Introduction, (Springer, Berlin Heidelberg, 1991).
328. G. A. Kohring, J. de Phys. I 6, 301 (1996).
329. R. Floriana and S. Galam, Eur. Phys. J. B 16, 189 (2000).
330. M. Pasquini and M. Serva, Phys. Rev. E 63, 056109 (2001).
331. J. Maskawa, Physica A 311, 563 (2002).
332. G. Toulouse, Commun. Phys. 2, 115 (1977).
333. H. Rieger, L. Santen, U. Blasum, M. Diehl, M. Jünger, and G. Rinaldi, J. Phys. A 29, 3939 (1996).
334. N. Kawashima and H. Rieger, Europhys. Lett. 39, 85 (1997).
335. A. K. Hartmann and A. P. Young, Phys. Rev B 64, 180404 (2001).
336. J. Houdayer, Eur. Phys. J. B 22, 479 (2001).
337. A. C. Carter, A. J. Bray, and M. A. Moore, Phys. Rev. Lett. 88, 077201 (2002).
338. I. Bieche, R. Maynard, R. Rammal, and J. P. Uhry, J. Phys. A 13, 2553 (1980).
339. U. Derigs and A. Metz, Math. Prog. 50, 113 (1991).
340. F. Barahona, R. Maynard, R. Rammal, and J. P. Uhry, J. Phys. A 15, 673 (1982).
341. W. J. Cook, W. H. Cunningham, W. R. Pulleyblank, and A. Schrijver, Combinatorial Optimization, (JohnWiley & Sons, New York 1998).
342. B. Korte and J. Vygen, Combinatorial Optimization -Theory and Algorithms, (Springer, Heidelberg 2000).
343. M. Palassini and A. P. Young, Phys. Rev. Lett. 85, 3017 (2000).
344. A. K. Hartmann and A. P. Young, Phys. Rev. B 66, 094419 (2002).
345. A. K. Hartmann and M. A. Moore, Phys. Rev. B 69, 104409 (2004).
346. N. Goldenfeld, Lectures on Phase Transitions and the Renormalization Group, (Addison Wesley, Reading (MA) 1992).
347. J. Cardy, Scaling and Renormalization in Statistical Physics, (Cambridge University Press, Cambridge 1996).
348. A. J. Bray and M. A. Moore, J. Phys. C 17, L463 (1984).
349. W. L. McMillan, J. Phys. C 17, 3179 (1984).
350. A. K. Hartmann, A. J. Bray, A. C. Carter, M. A. Moore, and A. P. Young, Phys. Rev. B 66, 224401 (2002).
351. W. L. McMillan, Phys. Rev. B 30, 476 (1984).
352. A. K. Hartmann, Phys. Rev. E 59, 84 (1999).
353. A. K. Hartmann, Phys. Rev. E 60, 5135 (1999).
354. K. Hukushima, preprint cond-mat/9903391 (1999).
355. A. J. Bray and M. A. Moore, in J. L. van Hemmen and I. Morgenstern (eds.), Glassy Dynamics and Optimization, (Springer, Berlin 1986).
356. D. S. Fisher and D. A. Huse, Phys. Rev. Lett. 56, 1601 (1986)
357. N. Kawashima and T. Aoki, J. Phys. Soc. Jpn., 69, Suppl. A, 169 (2000).
358. See also N. Kawashima, preprint cond-mat/9910366 (1999).
359. A. K. Hartmann and M. A. Moore, Phys. Rev. Lett. 90, 127201 (2003).