Torpid mixing of the Wang-Swendsen-Kotecký algorithm for sampling colorings

Journal of Discrete Algorithms

Volumn 3, Issue 1, 2005, Pages 92-100

  Łuczak, Tomasz ^a   Vigoda, Eric ^b  

^a ADAM MICKIEWICZ UNIVERSITY   (Poland)

^b UNIVERSITY OF EDINBURGH   (United Kingdom)

Author keywords

Coloring; Markov chain Monte Carlo; Randomized algorithms; Torpid mixing

Indexed keywords

COLORING; CONVERGENCE OF NUMERICAL METHODS; GRAPH THEORY; MARKOV PROCESSES; MIXING; MONTE CARLO METHODS; NUMBER THEORY; POLYNOMIALS;

MARKOV CHAIN MONTE CARLO; PLANAR GRAPHS; RANDOMIZED ALGORITHMS; TORPID MIXING;

ALGORITHMS;

EID: 13544249695     PISSN: 15708667     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jda.2004.05.002     Document Type: Article

References (14)

1. Aldous D.J., Fill J.A. Reversible Markov chains and random walks on graphs. Some chapters available at http://stat-www.berkeley.edu/pub/users/ aldous/book.html. in preparation
2. Burton J.K. Jr., Henley C.L. A constrained Potts antiferromagnet model with an interface representation. J. Phys. A. 30:(24):1997;8385-8413
3. Diaconis P., Saloff-Coste L. Comparison theorems for reversible Markov chains. Ann. Appl. Probab. 3:(3):1993;696-730
4. Ferreira S.J., Sokal A.D. Antiferromagnetic Potts models on the square lattice: A high-precision Monte Carlo study. J. Statist. Phys. 96:(3):1999;461-530
5. Glauber R. Time-dependent statistics of the Ising model. J. Math. Phys. 4:1963;294-307
6. Janson S., Łuczak T., Ruciński A. Random Graphs. 2000;Wiley, New York
7. Jerrum M., Sinclair A. The Markov chain Monte Carlo method: an approach to approximate counting and integration. Hochbaum D. Approximation Algorithms for NP-hard Problems. 1996;PWS Publishing Company
8. Kim J.H. On Brooks' theorem for sparse graphs. Combin. Probab. Comput. 4:1995;97-132
9. Lubin M., Sokal A.D. Comment on 'antiferromagnetic Potts models'. Phys. Rev. Lett. 71:1993;1778
10. Potts R. Some generalized order-disorder transformations. Proc. Camb. Phil. Soc. 48:1952;106-109
11. Vigoda E. Improved bounds for sampling colorings. 40th Annual Symposium on Foundations of Computer Science, New York. 1999;51-59
12. Wang J.S., Swendsen R.H., Kotecký R. Antiferromagnetic Potts models. Phys. Rev. Lett. 63:1989;109-112
13. Wang J.S., Swendsen R.H., Kotecký R. Three-state antiferromagnetic Potts models: A Monte Carlo study. Phys. Rev. B. 42:1990;2465-2474
14. Welsh D. Complexity: Knots, Colourings, and Counting. London Mathematical Society Lecture Note Series. vol. 186:1993