Approximate counting, uniform generation and rapidly mixing Markov chains
Information and Computation
A very simple algorithm for estimating the number of k-colorings of a low-degree graph
Random Structures & Algorithms
Balls and bins: a study in negative dependence
Random Structures & Algorithms
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Randomly coloring planar graphs with fewer colors than the maximum degree
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Fast mixing for independent sets, colorings, and other models on trees
Random Structures & Algorithms
Algorithmic Barriers from Phase Transitions
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
The Glauber Dynamics for Colourings of Bounded Degree Trees
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Reconstruction threshold for the hardcore model
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Rapid mixing of subset Glauber dynamics on graphs of bounded tree-width
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Phase transition for Glauber dynamics for independent sets on regular trees
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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We prove that the mixing time of the Glauber dynamics for random k-colorings of the complete tree with branching factor b undergoes a phase transition at k = b(1+ob(1))/ln b. Our main result shows nearly sharp bounds on the mixing time of the dynamics on the complete tree with n vertices for k = Cb/lnb colors with constant C. For C ≥ 1 we prove the mixing time is O(n1+ob(1) ln2 n). On the other side, for C O(n1/C+ob(1) ln2 n) and Ω(n1/C-ob(1)). The critical point C = 1 is interesting since it coincides (at least up to first order) to the so-called reconstruction threshold which was recently established by Sly. The reconstruction threshold has been of considerable interest recently since it appears to have close connections to the efficiency of certain local algorithms, and this work was inspired by our attempt to understand these connections in this particular setting.