A review of the Statistical Mechanics approach to Random Optimization Problems

We review the connection between statistical mechanics and the analysis of random optimization problems, with particular emphasis on the random k-SAT problem. We discuss and characterize the different phase transitions that are met in these problems, starting from basic concepts. We also discuss how statistical mechanics methods can be used to investigate the behavior of local search and decimation based algorithms.

[1]  Alan M. Frieze,et al.  Random graphs , 2006, SODA '06.

[2]  Michael I. Jordan,et al.  Advances in Neural Information Processing Systems 30 , 1995 .

[3]  École thématique du Cnrs,et al.  Slow Relaxations and nonequilibrium dynamics in condensed matter , 2003 .

[4]  Svante Janson,et al.  Random graphs , 2000, ZOR Methods Model. Oper. Res..

[5]  Jon Kleinberg,et al.  Proceedings of the thirty-eighth annual ACM symposium on Theory of computing , 2006, STOC 2006.

[6]  Anders Krogh,et al.  Introduction to the theory of neural computation , 1994, The advanced book program.

[7]  Elchanan Mossel,et al.  Complete Convergence of Message Passing Algorithms for Some Satisfiability Problems , 2006, Theory Comput..

[8]  October I Physical Review Letters , 2022 .

[9]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[10]  Armando Tacchella,et al.  Theory and Applications of Satisfiability Testing: 6th International Conference, Sat 2003, Santa Margherita Ligure, Italy, May 5-8 2003: Selected Revised Papers (Lecture Notes in Computer Science, 2919) , 2004 .

[11]  J. S. Wholey IEEE Transactions on Electronic Computers , 1963 .

[12]  M. Mézard,et al.  Spin Glass Theory and Beyond , 1987 .

[13]  Michael Krivelevich,et al.  Why almost all k-CNF formulas are easy , 2007 .

[14]  M. Talagrand,et al.  Bounds for diluted mean-fields spin glass models , 2004, math/0405357.

[15]  Gerhard Lakemeyer,et al.  Exploring artificial intelligence in the new millennium , 2003 .

[16]  P. Gács,et al.  Algorithms , 1992 .

[17]  Mike Mannion,et al.  Complex systems , 1997, Proceedings International Conference and Workshop on Engineering of Computer-Based Systems.

[18]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[19]  Noga Alon,et al.  The Probabilistic Method , 2015, Fundamentals of Ramsey Theory.

[20]  O. Bagasra,et al.  Proceedings of the National Academy of Sciences , 1914, Science.

[21]  Ericka Stricklin-Parker,et al.  Ann , 2005 .

[22]  I. Mazin,et al.  Theory , 1934 .

[23]  Amos Storkey,et al.  Advances in Neural Information Processing Systems 20 , 2007 .

[24]  V. Ramachandran Proceedings of the fourth annual ACM-SIAM symposium on Discrete algorithms , 1993 .

[25]  Hendrik B. Geyer,et al.  Journal of Physics A - Mathematical and General, Special Issue. SI Aug 11 2006 ?? Preface , 2006 .

[26]  D. Saad Europhysics Letters , 1997 .

[27]  S. Varadhan,et al.  Large deviations , 2019, Graduate Studies in Mathematics.

[28]  T. Liggett Interacting Particle Systems , 1985 .

[29]  Rémi Monasson A Generating Function Method for the Average-Case Analysis of DPLL , 2005, APPROX-RANDOM.

[30]  Rajeev Motwani,et al.  Randomized algorithms , 1996, CSUR.

[31]  Kenneth Steiglitz,et al.  Combinatorial Optimization: Algorithms and Complexity , 1981 .

[32]  M. Talagrand,et al.  Spin Glasses: A Challenge for Mathematicians , 2003 .

[33]  J. Herskowitz,et al.  Proceedings of the National Academy of Sciences, USA , 1996, Current Biology.