Mixing properties of the Swendsen-Wang process on classes of graphs

Random Structures and Algorithms

Volumn 15, Issue 3-4, 1999, Pages 242-261

  Cooper, Colin ^a   Frieze, Alan M ^b  

^a QUEEN MARY UNIVERSITY OF LONDON   (United Kingdom)

^b CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033438251     PISSN: 10429832     EISSN: None     Source Type: Journal    
DOI: 10.1002/(sici)1098-2418(199910/12)15:3/4<242::aid-rsa4>3.0.co;2-c     Document Type: Article

References (17)

1. D. Aldous and J. Fill, Reversible Markov chains and random walks on graphs, in preparation.
2. R. Baxter, Exactly Solved Models in Statistical Mechanics, Academic, New York, 1982.
3. R. Bubley and M. Dyer, Path coupling: A technique for proving rapid mixing in Markov chains, Proc 38th Annual IEEE Symp on Foundations of Computer Science, 1997.
4. M. Dyer, Private communication, 1998.
5. R.G. Edwards and A.D. Sokal, Generalizations of the Fortuin-Kasteleyn-Swendsen-Wang representation and Monte Carlo algorithm, Phys Rev D, 38 (1988), 2009-2012.
6. C. Fortuin and P. Kasteleyn, On the random cluster model I: Introduction and relation to other models, Physica, 57 (1972), 536-564.
7. V. Gore and M. Jerrum, The Swendsen-Wang process does not always mix rapidly, Proc 29th Annual ACM Symp on Theory of Computing, 1997, pp. 674-681.
8. M. Huber, Efficient exact sampling from the Ising model using Swendsen-Wang, Proc 10th Annual ACM-SIAM Symp on Discrete Algorithms, 1999.
9. M. Jerrum, A very simple algorithm for estimating the number of K-colorings of a low degree graph, Random Struct Alg, 7 (1995), 157-165.
10. M. Jerrum and A. Sinclair, The Markov chain Monte Carlo method: An approach to approximate counting and integration, Approximation Algorithms for NP-Hard Problems, D. Hochbaum (Editor), PWS-Kent, Boston, 1996, pp. 482-520.
11. X.-J. Li and A. D. Sokal, Rigorous lower bound on the dynamic critical exponents of the Swendsen-Wang algorithm, Phys Rev Lett, 63 (1989), 827-830.
12. J.G. Oxley and D.J.A. Welsh, Tutte polynomials computable in polynomial time, Discrete Math, 109 (1992), 185-192.
13. R. Potts, Some generalized order-disorder transformations, Proc Cambridge Philos Soc, 48 (1952), 106-109.
14. T.S. Ray, P. Tamayo, and W. Klein, Mean-field study of the Swendsen-Wang dynamics, Phys Rev A 39 (1989), 5949-5953.
15. A. Sinclair, Algorithms for Random Generation and Counting, Birkhauser, Boston, 1993.
16. R. Swendsen and J-S. Wang, Non-universal critical dynamics in Monte-Carlo simulation, Phys Rev Lett, 58 (1987), 86-88.
17. D.J.A. Welsh, Complexity: Knots, Colorings and Counting, London Mathematical Society Lecture Note Series, Cambridge Univ. Press, Cambridge, UK, 1993, Vol. 186.