Introduction to Phase Transitions in Random Optimization Problems

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

[2]  Hilary Putnam,et al.  A Computing Procedure for Quantification Theory , 1960, JACM.

[3]  Donald Ervin Knuth,et al.  The Art of Computer Programming , 1968 .

[4]  Donald E. Knuth,et al.  The art of computer programming: V.1.: Fundamental algorithms , 1997 .

[5]  D. Thouless,et al.  Stability of the Sherrington-Kirkpatrick solution of a spin glass model , 1978 .

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

[7]  Béla Bollobás,et al.  Random Graphs , 1985 .

[8]  H. Orland.  Mean-field theory for optimization problems , 1985 .

[9]  M. Mézard,et al.  Replicas and optimization , 1985 .

[10]  Ming-Te Chao,et al.  Probabilistic Analysis of Two Heuristics for the 3-Satisfiability Problem , 1986, SIAM J. Comput..

[11]  P. Anderson,et al.  Application of statistical mechanics to NP-complete problems in combinatorial optimisation , 1986 .

[12]  M. Mézard,et al.  A replica analysis of the travelling salesman problem , 1986 .

[13]  M. Mézard,et al.  On the solution of the random link matching problems , 1987 .

[14]  Endre Szemerédi,et al.  Many hard examples for resolution , 1988, JACM.

[15]  W. Krauth,et al.  Storage capacity of memory networks with binary couplings , 1989 .

[16]  G. Parisi,et al.  On a mechanism for explicit replica symmetry breaking , 1989 .

[17]  Daniel J. Amit,et al.  Modeling brain function: the world of attractor neural networks, 1st Edition , 1989 .

[18]  David Aldous.  The harmonic mean formula for probabilities of unions: applications to sparse random graphs , 1989, Discret. Math..

[19]  Ming-Te Chao,et al.  Probabilistic analysis of a generalization of the unit-clause literal selection heuristics for the k satisfiability problem , 1990, Inf. Sci..

[20]  Christos H. Papadimitriou,et al.  Proceedings of the 32nd annual symposium on Foundations of computer science , 1991 .

[21]  Peter L. Hammer,et al.  Discrete Applied Mathematics , 1993 .

[22]  Cugliandolo,et al.  Analytical solution of the off-equilibrium dynamics of a long-range spin-glass model. , 1993, Physical review letters.

[23]  Rajeev Motwani,et al.  Randomized Algorithms , 1995, SIGA.

[24]  Rajeev Motwani,et al.  Randomized Algorithms , 1995, SIGA.

[25]  N. Wormald.  Differential Equations for Random Processes and Random Graphs , 1995 .

[26]  Monasson.  Structural glass transition and the entropy of the metastable states. , 1995, Physical Review Letters.

[27]  Alan M. Frieze,et al.  Analysis of Two Simple Heuristics on a Random Instance of k-SAT , 1996, J. Algorithms.

[28]  R. Monasson,et al.  Statistical Mechanics of the K--Satisfiability Model , 1996, cond-mat/9606215.

[29]  Herbert S. Wilf,et al.  Algorithms and Complexity , 1994, Lecture Notes in Computer Science.

[30]  Amir Dembo,et al.  Large Deviations Techniques and Applications , 1998 .

[31]  S. Mertens.  Phase Transition in the Number Partitioning Problem , 1998, cond-mat/9807077.

[32]  R. Monasson.  Optimization problems and replica symmetry breaking in finite connectivity spin glasses , 1997, cond-mat/9707089.

[33]  Rémi Monasson,et al.  THE EUROPEAN PHYSICAL JOURNAL B c○ EDP Sciences , 1999 .

[34]  Nadia Creignou,et al.  Satisfiability Threshold for Random XOR-CNF Formulas , 1999, Discret. Appl. Math..

[35]  Mertens.  Random costs in combinatorial optimization , 1999, Physical review letters.

[36]  R. Monasson,et al.  Statistical physics analysis of the computational complexity of solving random satisfiability problems using backtrack algorithms , 2000, cond-mat/0012191.

[37]  Alexander K. Hartmann,et al.  The number of guards needed by a museum: A phase transition in vertex covering of random graphs , 2000, Physical review letters.

[38]  Dimitris Achlioptas,et al.  Lower bounds for random 3-SAT via differential equations , 2001, Theor. Comput. Sci..

[39]  Christian Van den Broeck,et al.  Statistical Mechanics of Learning , 2001 .

[40]  M. Mézard,et al.  The Bethe lattice spin glass revisited , 2000, cond-mat/0009418.

[41]  Riccardo Zecchina,et al.  Simplest random K-satisfiability problem , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[42]  Uwe Schöning,et al.  A Probabilistic Algorithm for k -SAT Based on Limited Local Search and Restart , 2002, Algorithmica.

[43]  S Cocco,et al.  Trajectories in phase diagrams, growth processes, and computational complexity: how search algorithms solve the 3-satisfiability problem. , 2001, Physical review letters.

[44]  Stephan Mertens,et al.  A physicist's approach to number partitioning , 2000, Theor. Comput. Sci..

[45]  Alexander K. Hartmann,et al.  Typical solution time for a vertex-covering algorithm on finite-connectivity random graphs , 2001, Physical review letters.

[46]  D. Aldous.  The ζ(2) limit in the random assignment problem , 2000, Random Struct. Algorithms.

[47]  Alexander K. Hartmann,et al.  Statistical mechanics perspective on the phase transition in vertex covering of finite-connectivity random graphs , 2000, Theor. Comput. Sci..

[48]  Riccardo Zecchina,et al.  Coloring random graphs , 2002, Physical review letters.

[49]  Armando Tacchella,et al.  Theory and Applications of Satisfiability Testing , 2003, Lecture Notes in Computer Science.

[50]  Nadia Creignou,et al.  Smooth and sharp thresholds for random k-XOR-CNF satisfiability , 2003, RAIRO Theor. Informatics Appl..

[51]  R. Monasson,et al.  Relaxation and metastability in a local search procedure for the random satisfiability problem. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[52]  R. Monasson,et al.  Rigorous decimation-based construction of ground pure states for spin-glass models on random lattices. , 2002, Physical review letters.

[53]  Alexander K. Hartmann,et al.  Solving satisfiability problems by fluctuations: The dynamics of stochastic local search algorithms , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[54]  Eli Ben-Sasson,et al.  Analysis of the Random Walk Algorithm on Random -CNFs , 2003 .

[55]  Nadia Creignou,et al.  Approximating The Satisfiability Threshold For Random K-Xor-Formulas , 2003, Comb. Probab. Comput..

[56]  M. Mézard,et al.  Two Solutions to Diluted p-Spin Models and XORSAT Problems , 2003 .

[57]  Michael Molloy,et al.  A sharp threshold in proof complexity yields lower bounds for satisfiability search , 2004, J. Comput. Syst. Sci..

[58]  公庄 庸三.  Discrete math = 離散数学 , 2004 .

[59]  Assaf Naor,et al.  Rigorous location of phase transitions in hard optimization problems , 2005, Nature.

[60]  Rémi Monasson,et al.  Criticality and universality in the unit-propagation search rule , 2005, ArXiv.

[61]  Andrea Montanari,et al.  From Large Scale Rearrangements to Mode Coupling Phenomenology in Model Glasses , 2005 .

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

[63]  B. Bollobás,et al.  Combinatorics, Probability and Computing , 2006 .

[64]  Dan Suciu,et al.  Journal of the ACM , 2006 .

[65]  P. S. Dwyer.  Annals of Applied Probability , 2006 .

[66]  Rémi Monasson,et al.  Can rare SAT formulas be easily recognized? On the efficiency of message passing algorithms for K-SAT at large clause-to-variable ratios , 2006, ArXiv.

[67]  Florent Krzakala,et al.  A Landscape Analysis of Constraint Satisfaction Problems , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[68]  Andrea Montanari,et al.  Gibbs states and the set of solutions of random constraint satisfaction problems , 2006, Proceedings of the National Academy of Sciences.

[69]  L. Kirousis,et al.  How to prove conditional randomness using the Principle of Deferred Decisions , 2008 .

[70]  R. Rosenfeld.  Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.