Random generation of combinatorial structures from a uniform
Theoretical Computer Science
The Markov chain Monte Carlo method: an approach to approximate counting and integration
Approximation algorithms for NP-hard problems
Some optimal inapproximability results
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Approximately counting up to four (extended abstract)
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
The complexity of choosing an H-colouring (nearly) uniformly at random
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Counting H-colorings of partial k-trees
Theoretical Computer Science
Counting H-Colorings of Partial k-Trees
COCOON '01 Proceedings of the 7th Annual International Conference on Computing and Combinatorics
On the relative complexity of approximate counting problems
APPROX '00 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization
Counting independent sets up to the tree threshold
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Rapid mixing of Gibbs sampling on graphs that are sparse on average
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Faster Algorithms for Sampling and Counting Biological Sequences
SPIRE '09 Proceedings of the 16th International Symposium on String Processing and Information Retrieval
Some Remarks Concerning the Algorithmic Analysis of Gene Regulatory Networks
Electronic Notes in Theoretical Computer Science (ENTCS)
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We prove two results concerning approximate counting of independent sets in graphs with constant maximum degree \math. The first implies that the Monte Carlo Markov chain technique is likely to fail if \math. The second shows that no fully polynomial randomized approximation scheme can exist for \math, unless P =NP under randomized reductions.