Random generation of embedded graphs and an extension to Dobrushin uniqueness (extended abstract)
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Recovery time of dynamic allocation processes
Proceedings of the tenth annual ACM symposium on Parallel algorithms and architectures
Delayed path coupling and generating random permutations via distributed stochastic processes
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Faster random generation of linear extensions
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Balanced allocations: the heavily loaded case
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Random three-dimensional tilings of Aztec octahedra and tetrahedra: an extension of domino tilings
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
The Glauber dynamics on colourings of a graph with high girth and maximum degree
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Very rapid mixing of the Glauber dynamics for proper colorings on bounded-degree graphs
Random Structures & Algorithms
Decomposition Methods and Sampling Circuits in the Cartesian Lattice
MFCS '01 Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science
Random dyadic tilings of the unit square
Random Structures & Algorithms - Special issue: Proceedings of the tenth international conference "Random structures and algorithms"
Randomly coloring graphs of girth at least five
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Markovian Coupling vs. Conductance for the Jerrum-Sinclair Chain
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Random generation of 2×2×...×2×Jcontingency tables
Theoretical Computer Science
Efficiency test of pseudorandom number generators using random walks
Journal of Computational and Applied Mathematics
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
Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing
Combinatorial criteria for uniqueness of Gibbs measures
Random Structures & Algorithms
Accelerating simulated annealing for the permanent and combinatorial counting problems
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Disjoint Decomposition of Markov Chains and Sampling Circuits in Cayley Graphs
Combinatorics, Probability and Computing
Parsing Images into Regions, Curves, and Curve Groups
International Journal of Computer Vision
Coupling and self-stabilization
Distributed Computing - Special issue: DISC 04
Approximate/perfect samplers for closed Jackson networks
WSC '05 Proceedings of the 37th conference on Winter simulation
On the expected time for Herman's probabilistic self-stabilizing algorithm
Theoretical Computer Science
Randomly coloring sparse random graphs with fewer colors than the maximum degree
Random Structures & Algorithms
Path coupling without contraction
Journal of Discrete Algorithms
Balanced allocations: the weighted case
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Random Structures & Algorithms
Dobrushin conditions and systematic scan
Combinatorics, Probability and Computing
Sampling Eulerian orientations of triangular lattice graphs
Journal of Discrete Algorithms
A Polynomial-Time Perfect Sampler for the Q-Ising with a Vertex-Independent Noise
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
An optimization-based sampling scheme for phylogenetic trees
RECOMB'11 Proceedings of the 15th Annual international conference on Research in computational molecular biology
A polynomial-time perfect sampler for the Q-Ising with a vertex-independent noise
Journal of Combinatorial Optimization
UAI'02 Proceedings of the Eighteenth conference on Uncertainty in artificial intelligence
Stopping times, metrics and approximate counting
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
On weighted balls-into-bins games
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Provable anonymity for networks of mixes
IH'05 Proceedings of the 7th international conference on Information Hiding
ICISC'04 Proceedings of the 7th international conference on Information Security and Cryptology
Dobrushin conditions and systematic scan
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Randomly colouring graphs with girth five and large maximum degree
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Sampling colourings of the triangular lattice
Random Structures & Algorithms
Two approaches to understanding when constraints help clustering
Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining
Decentralized dynamics for finite opinion games
SAGT'12 Proceedings of the 5th international conference on Algorithmic Game Theory
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The main technique used in algorithm design for approximating #P-hard counting problems is the Markov chain Monte Carlo method. At the heart of the method is the study of the convergence (mixing) rates of particular Markov chains of interest. In this paper we illustrate a new approach to the coupling technique, which we call path coupling, for bounding mixing rates. Previous applications of coupling have required detailed insights into the combinatorics of the problem at hand, and this complexity can make the technique extremely difficult to apply successfully. Path coupling helps to minimize the combinatorial difficulty and in all cases provides simpler convergence proofs than does the standard coupling method. However the true power of the method is that the simplification obtained may allow coupling proofs which were previously unknown, or provide significantly better bounds than those obtained using the standard method. We apply the path coupling method to several hard combinatorial problems, obtaining new or improved results. We examine combinatorial problems such as graph colouring and TWICE-SAT, and problems from statistical physics, such as the antiferromagnetic Potts model and the hard-core lattice gas model. In each case we provide either a proof of rapid mixing where none was known previously, or substantial simplification of existing proofs with consequent gains in the performance of the resulting algorithms.