Statistical mechanics methods and phase transitions in optimization problems

Theoretical Computer Science

Volumn 265, Issue 1-2, 2001, Pages 3-67

  Martin, Olivier C ^a   Monasson, Rémi ^b   Zecchina, Riccardo ^c  

^a UNIVERSITÉ PARIS SUD   (France)

^b UNIVERSITY OF CHICAGO   (United States)

^c ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS   (Italy)

Author keywords

Optimizations; Phase transitions; Random graph; Satisfiability; Statistical physsics; Traveling salesman

Indexed keywords

COMBINATORIAL MATHEMATICS; COMPUTER SCIENCE; DECISION THEORY; GRAPH THEORY; PHASE TRANSITIONS; PROBABILISTIC LOGICS; RANDOM NUMBER GENERATION; STATISTICAL MECHANICS; TRAVELING SALESMAN PROBLEM;

OPTIMIZATION PROBLEMS; STATISTICAL PHYSICS;

PROBLEM SOLVING;

EID: 0034887189     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-3975(01)00149-9     Document Type: Article

References (84)

1. The zeta(2) limit in the random assignment problem
2. On the solution of traveling salesman problems
3. Graph bipartitioning and statistical mechanics
4. The shortest path through many points
5. A variational description of the ground-state structure in random satisfiability problems
6. Length of prime implicants and number of solutions of random cnf formulas
7. On the satisfiability and maximum satisfiability of random 3-cnf formulas
8. Extensive numerical simulations of weighted matchings: Total length and distribution of links in the optimal solution
9. The scaling window of the 2-sat transition
10. Thermodynamical approach to the traveling salesman problem: An efficient simulation algorithm
11. Probabilistic analysis of a generalization of the unit-clause literal selection heuristics for the k-satisfiability
12. Mick gets some (the odds are on his side)
13. Trajectories in phase diagrams, growth processes and computational complexity: How search algorithms solve the 3-satisfiability problem
14. The complexity of theorem-proving procedures
15. Replica symmetry breaking in finite connectivity systems: A large connectivity expansion at finite and zero temperature
16. Replica symmetry breaking in weak connectivity systems
17. Exact solution of the random bipartite matching model
18. Frontiers in problem solving: Phase transitions and complexity
19. Complexity of learning in artificial neural networks
20. Application of statistical mechanics to NP-complete problems in combinatorial optimization
21. A threshold for unsatisfiability
22. The finite connectivity spin glass: Investigation of replica symmetry breaking of the ground-state
23. Statistical mechanics perspective on the phase transition in vertex covering of finite-connectivity random graphs
24. Comparing mean field and Euclidean matching problems
25. Asymptotic experimental analysis for the Held-Karp traveling salesman bound
26. The traveling salesman problem: A case study in local optimization
27. Mean-field theory of spin-glasses with finite coordination number
28. A patching algorithm for the nonsymmetric travelling salesman problem
29. Optimization by simulated annealing
30. Critical behaviour in the satisfiability of random boolean expressions
31. The cavity method and the travelling-salesman problem
32. Branch-and-bound methods: A survey
33. Phase coexistence and finite size scaling in random combinatorial problems
34. Computer solutions of the traveling salesman problem
35. A physicist's approach to number partitioning
36. Mean-field equations for the matching and the travelling salesman problem
37. On the solution of the random link matching problems
38. Mean-field theory of randomly frustrated systems with finite connectivity
39. Hard and easy distributions of sat problems
40. Optimization problems and replica symmetry breaking in finite connectivity spin glasses
41. Entropy of the K-satisfiability problem
42. Statistical mechanics of the random K-Sat problem
43. Tricritical points in random combinatorics: The (2+p)-SAT case
44. Computational complexity from 'characteristic' phase transitions
45. 2+p-sat: Relation of typical-case complexity to thenature of the phase transition
46. Large deviations in random graphs
47. On the stability of randomly frustrated systems with finite connectivity
48. A branch and cut algorithm for the resolution of large-scale symmetric traveling salesman problems
49. Several results on the finite-size corrections in the Sherrington-Kirkpatrick spin glass model
50. Finite size and dimensional dependence in the Euclidean traveling salesman problem
51. The stochastic traveling salesman problem: Finite size scaling and the cavity prediction
52. On the travelling salesperson problem in many dimensions
53. Martingale inequalities and NP-complete problems
54. The simplest k-satisfiability model
55. Frustrated systems: Ground state properties via combinatorial optimization
56. Cut size statistics of graph bisection heuristics
57. Local search strategies for satisfiability testing
58. Phase coexistence in a single DNA molecule
59. Rigorous low temperature results for the p-spin mean field spin glass model
60. On the statistical mechanics of optimization problems of the travelling salesman type
61. Phase diagrams for dilute spin-glasses
62. The Potts model