SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Fast mixing for independent sets, colorings and other models on trees
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
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
Accelerating simulated annealing for the permanent and combinatorial counting problems
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Rapidly Mixing Markov Chains with Applications in Computer Science and Physics
Computing in Science and Engineering
Randomly coloring sparse random graphs with fewer colors than the maximum degree
Random Structures & Algorithms
Fast mixing for independent sets, colorings, and other models on trees
Random Structures & Algorithms
Random Structures & Algorithms
Faster Algorithms for Sampling and Counting Biological Sequences
SPIRE '09 Proceedings of the 16th International Symposium on String Processing and Information Retrieval
On the hardness of counting and sampling center strings
SPIRE'10 Proceedings of the 17th international conference on String processing and information retrieval
Approximate counting via correlation decay in spin systems
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Randomly colouring graphs with girth five and large maximum degree
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
On the Hardness of Counting and Sampling Center Strings
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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We study a simple Markov chain, known as the Glauber dynamics, for randomly sampling (proper) k-colorings of an input graph G on n vertices with maximum degree \Delta and girth g. We prove the Glauber dynamics is close to the uniform distribution after 0(n log n) steps whenever k (1 + \varepsilon)\Delta for all \varepsilon 0, assuming g 驴 9 and \Delta= \Omega (\log n). The best previously known bounds were k 11\Delta/6 for general graphs, and k 1.489\Delta for graphs satisfying girth and maximum degree requirements.Our proof relies on the construction and analysis of a non-Markovian coupling. This appears to be the first application of a non-Markovian coupling to substantially improve upon known results.