Computational transition at the uniqueness threshold

Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

Volumn , Issue , 2010, Pages 287-296

  Sly, Allan ^a  

^a MICROSOFT RESEARCH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATION THEORY; FORESTRY; GRAPHIC METHODS; HEURISTIC METHODS; LATTICE THEORY; METHOD OF MOMENTS; POLYNOMIAL APPROXIMATION; PROBABILITY DISTRIBUTIONS; SAMPLING; STATISTICAL PHYSICS;

APPROXIMATE COUNTING; COUNTING INDEPENDENT SETS; POLYNOMIAL TIME APPROXIMATION SCHEMES; RECONSTRUCTION PROBLEMS; SECOND MOMENT METHODS; THEORETICAL COMPUTER SCIENCE; THEORETICAL PHYSICIST; WEIGHTED INDEPENDENT SETS;

TREES (MATHEMATICS);

EID: 78751492707     PISSN: 02725428     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/FOCS.2010.34     Document Type: Conference Paper

References (37)

1. D. Achlioptas and A. Coja-Oghlan, Algorithmic barriers from phase transitions, IEEE 49th Annual IEEE Symposium on Foundations of Computer Science, 2008. FOCS'08, 2008, pp. 793-802.
2. D. J. Aldous, The ζ(2) limit in the random assignment problem, Random Structures and Algorithms 18 (2001), 381-418.
3. N. Berger, C. Kenyon, E. Mossel, and Y. Peres, Glauber dynamics on trees and hyperbolic graphs, Probability Theory and Related Fields 131 (2005), 311-340.
4. P. Berman and T. Fujito, On approximation properties of the independent set problem for low degree graphs, Theory of Computing Systems 32 (1999), 115-132.
5. N. Bhatnagar, A. Sly, and P. Tetali, Reconstruction Threshold for the Hardcore Model, arXiv:1004.3531 (2010).
6. N. Bhatnagar, J. Vera, E. Vigoda, and D. Weitz, Reconstruction for colorings on trees, To appear in SIAM J. on Discrete Math. (2008).
7. C. Borgs, J. Chayes, E. Mossel, and S. Roch, The Kesten-Stigum reconstruction bound is tight for roughly symmetric binary channels, Foundations of Computer Science, 2006. FOCS'06. 47th Annual IEEE Symposium on, 2006, pp. 518-530.
8. A. Dembo and A. Montanari, Ising models on locally tree-like graphs, Ann. Appl. Probab 20 (2010), 565-592.
9. M. Dyer, A. Frieze, and M. Jerrum, On Counting Independent Sets in Sparse Graphs, SIAM Journal on Computing 31 (2002), 1527.
10. M. Dyer and C. Greenhill, On Markov Chains for Independent Sets, Journal of Algorithms 35 (2000), 17-49.
11. D. Galvin and P. Tetali, Slow mixing of Glauber dynamics for the hard-core model on regular bipartite graphs, Random Structures and Algorithms 28 (2006), 427-443.
12. H. O. Georgii, Gibbs measures and phase transitions, Walter de Gruyter, 1988.
13. C. Greenhill, The complexity of counting colourings and independent sets in sparse graphs and hypergraphs, Computational Complexity 9 (2000), 52-72.
14. L. A. Goldberg and M. Jerrum, Approximating the partition function of the ferromagnetic Potts model, Arxiv:1002.0986 (2010).
15. S. Janson and E. Mossel, Robust reconstruction on trees is determined by the second eigenvalue, Annals of Probability 32 (2004), 2630-2649.
16. S. Janson, T. Łuczak, and A. Ruciński, Random graphs, Wiley, 2000.
17. M. Jerrum and A. Sinclair, Polynomial-time approximation algorithms for the Ising model, Automata, Languages and Programming (1990), 462-475.
18. F. Kelly, Stochastic models of computer communication systems, Journal of the Royal Statistical Society. Series B (Methodological) 47 (1985), no. 3, 379-395.
19. H. Kesten and B. P. Stigum, Additional limit theorems for indecomposable multidimensional Galton-Watson processes, The Annals of Mathematical Statistics 37 (1966), 1463-1481.
20. F. Krz̧akała, A. Montanari, F. Ricci-Tersenghi, G. Semerjian, and L. Zdeborová, Gibbs states and the set of solutions of random constraint satisfaction problems, Proceedings of the National Academy of Sciences 104 (2007), 10318.
21. M. Luby and E. Vigoda, Fast convergence of the Glauber dynamics for sampling independent sets, Random Structures and Algorithms 15 (1999), 229-241.
22. F. Martinelli and E. Olivieri, Approach to equilibrium of Glauber dynamics in the one phase region. I. The attractive case, Comm. Math. Phys. 161 (1994), no. 3, 447-486.
23. F. Martinelli, A. Sinclair, and D. Weitz, Fast mixing for independent sets, colorings, and other models on trees, Random Structures Algorithms 31 (2007), 134-172.
24. M. Mezard and A. Montanari, Information, physics, and computation, Oxford University Press, USA, 2009.
25. M. Mezard, G. Parisi, and M. A. Virasoro, Spin glass theory and beyond, World scientific, Singapore, 1987.
26. E. Mossel, Survey: information flow on trees, Graphs, morphisms, and statistical physics: DIMACS Workshop Graphs, Morphisms and Statistical Physics, March 19-21, 2001, DIMACS Center, 2004, pp. 155-170.
27. A. Montanari, E. Mossel, and A. Sly, The weak limit of Ising models on locally tree-like graphs, ArXiv:0912.0719 (2009).
28. E. Mossel and Y. Peres, Information flow on trees, Annals of Applied Probability 13 (2003), 817-844.
29. E. Mossel and A. Sly, Exact Thresholds for Ising-Gibbs Samplers on General Graphs, arXiv:0903.2906 (2009).
30. E. Mossel, D. Weitz, and N. Wormald, On the hardness of sampling independent sets beyond the tree threshold, Probability Theory and Related Fields 143 (2009), 401-439.
31. A. Sinclair and M. Jerrum, Approximate counting, uniform generation and rapidly mixing Markov chains, Information and Computation 82 (1989), 93-133.
32. A. Sokal, A personal list of unsolved problems concerning lattice gases and antiferromagnetic Potts models, Markov Process. Related Fields 7 (2001), 21-38.
33. A. Sly, Uniqueness thresholds on trees versus graphs, The Annals of Applied Probability 18 (2008), no. 5, 1897-1909.
34. A. Sly, Reconstruction for the Potts model, Proceedings of the 41st annual ACM symposium on Theory of computing, 2009, pp. 581-590.
35. M. Talagrand, The Parisi formula, Annals of Mathematics 163 (2006), 221-264.
36. D. Weitz, Counting independent sets up to the tree threshold, STOC '06: Proceedings of the thirty-eighth annual ACM symposium on Theory of computing (2006), pp. 140-149.
37. N. C. Wormald, Models of random regular graphs, London Mathematical Society Lecture Note Series (1999), 239-298.