A very simple algorithm for estimating the number of k-colorings of a low-degree graph
Random Structures & Algorithms
A more rapidly mixing Markov chain for graph colorings
proceedings of the eighth international conference on Random structures and algorithms
Graph orientations with no sink and an approximation for a hard case of #SAT
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Fast convergence of the Glauber dynamics for sampling independent sets
Random Structures & Algorithms - Special issue on statistical physics methods in discrete probability, combinatorics, and theoretical computer science
On Markov chains for independent sets
Journal of Algorithms
The complexity of counting graph homomorphisms
Proceedings of the ninth international conference on on Random structures and algorithms
Approximating coloring and maximum independent sets in 3-uniform hypergraphs
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Randomized algorithms: approximation, generation, and counting
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The complexity of counting colourings and independent sets in sparse graphs and hypergraphs
Computational Complexity
Random Structures & Algorithms
Colouring graphs when the number of colours is nearly the maximum degree
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
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An Extension of Path Coupling and Its Application to the Glauber Dynamics for Graph Colorings
SIAM Journal on Computing
On Counting Independent Sets in Sparse Graphs
SIAM Journal on Computing
The Hardness of 3 - Uniform Hypergraph Coloring
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Approximating Maximum Independent Sets in Uniform Hypergraphs
MFCS '98 Proceedings of the 23rd International Symposium on Mathematical Foundations of Computer Science
A new multilayered PCP and the hardness of hypergraph vertex cover
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Uniquely Colourable Graphs and the Hardness of Colouring Graphs of Large Girth
Combinatorics, Probability and Computing
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Randomly Coloring Constant Degree Graphs
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Corrigendum: the complexity of counting graph homomorphisms
Random Structures & Algorithms
Approximate counting via correlation decay in spin systems
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
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We analyse the mixing time of Markov chains using path coupling with stopping times. We apply this approach to two hypergraph problems. We show that the Glauber dynamics for independent sets in a hypergraph mixes rapidly as long as the maximum degree Δ of a vertex and the minimum size m of an edge satisfy m ≥ 2Δ + 1. We also show that the Glauber dynamics for proper q-colorings of a hypergraph mixes rapidly if m ≥ 4 and q Δ, and if m = 3 and q ≥ 1.65Δ. We give related results on the hardness of exact and approximate counting for both problems. © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2008