Random generation of combinatorial structures from a uniform
Theoretical Computer Science
A random polynomial-time algorithm for approximating the volume of convex bodies
Journal of the ACM (JACM)
Algorithms for random generation and counting: a Markov chain approach
Algorithms for random generation and counting: a Markov chain approach
A very simple algorithm for estimating the number of k-colorings of a low-degree graph
Random Structures & Algorithms
Random walks and an O*(n5) volume algorithm for convex bodies
Random Structures & Algorithms
A polynomial-time approximation algorithm for the permanent of a matrix with non-negative entries
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
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
Randomly coloring graphs of girth at least five
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Path coupling: A technique for proving rapid mixing in Markov chains
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
A Non-Markovian Coupling for Randomly Sampling Colorings
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Strong Spatial Mixing for Lattice Graphs with Fewer Colours
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Randomly Coloring Constant Degree Graphs
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Mixing in time and space for lattice spin systems: A combinatorial view
Random Structures & Algorithms - Isaac Newton Institute Programme “Computation, Combinatorics and Probability”: Part II
Counting independent sets up to the tree threshold
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
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
Torpid mixing of local Markov chains on 3-colorings of the discrete torus
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
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
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We present an improved coupling technique for analyzing the mixing time of Markov chains. Using our technique, we simplify and extend previous results for sampling colorings and independent sets. Our approach uses properties of the stationary distribution to avoid worst-case configurations which arise in the traditional approach.As an application, we show that for k/Δ 1.764, the Glauber dynamics on k-colorings of a graph on n vertices with maximum degree Δ converges in O(n log n) steps, assuming Δ = Ω(log n) and that the graph is triangle-free. Previously, girth ≥ 5 was needed.As a second application, we give a polynomial-time algorithm for sampling weighted independent sets from the Gibbs distribution of the hard-core lattice gas model at fugacity λ e/Δ, on a regular graph G on n vertices of degree Δ = Ω(log n) and girth ≥ 6. The best known algorithm for general graphs currently assumes λ