Coupling with the stationary distribution and improved sampling for colorings and independent sets
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Counting without sampling: new algorithms for enumeration problems using statistical physics
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Randomly coloring sparse random graphs with fewer colors than the maximum degree
Random Structures & Algorithms
Randomly coloring planar graphs with fewer colors than the maximum degree
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Correlation decay and deterministic FPTAS for counting list-colorings of a graph
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Fast mixing for independent sets, colorings, and other models on trees
Random Structures & Algorithms
Rapid mixing of Gibbs sampling on graphs that are sparse on average
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Path coupling using stopping times and counting independent sets and colorings in hypergraphs
Random Structures & Algorithms
Random Structures & Algorithms
Reconstruction for the Potts model
Proceedings of the forty-first annual ACM symposium on Theory of computing
Approximate counting via correlation decay in spin systems
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Stopping times, metrics and approximate counting
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Path coupling using stopping times
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
Randomly colouring graphs with girth five and large maximum degree
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
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We study a simple Markov chain, known as the Glauber dynamics, for generating a random k-coloring of a n-vertex graph with maximum degree 驴. We prove that the dynamics converges to a random coloring after 0(n log n) steps assuming k 驴 k_0 for some absolute constnat k_0, and either: (i) {k \mathord{\left/ {\vphantom {k \Delta }} \right. \kern-\nulldelimiterspace} \Delta } 驴* 驴 1.763 and the girth g 驴 5, or (ii) {k \mathord{\left/ {\vphantom {k \Delta }} \right. \kern-\nulldelimiterspace} \Delta } β* 驴 1.489 and the girth g 驴 6. Previous results on this problem applied when k = 驴(log n), or when k 11驴/6 for general graphs.