Random generation of combinatorial structures from a uniform
Theoretical Computer Science
NP is as easy as detecting unique solutions
Theoretical Computer Science
Monte-Carlo approximation algorithms for enumeration problems
Journal of Algorithms
PP is as hard as the polynomial-time hierarchy
SIAM Journal on Computing
Algorithms for random generation and counting: a Markov chain approach
Algorithms for random generation and counting: a Markov chain approach
Descriptive complexity of #P functions
Journal of Computer and System Sciences
On the hardness of approximate reasoning
Artificial Intelligence
The Markov chain Monte Carlo method: an approach to approximate counting and integration
Approximation algorithms for NP-hard problems
The complexity of counting graph homomorphisms (extended abstract)
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
On the Difference Between One and Many (Preliminary Version)
Proceedings of the Fourth Colloquium on Automata, Languages and Programming
On Counting Independent Sets in Sparse Graphs
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
The complexity of approximate counting
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
On the Relative Complexity of Approximate Counting Problems
On the Relative Complexity of Approximate Counting Problems
Rapidly Mixing Markov Chains for Dismantleable Constraint Graphs
RANDOM '02 Proceedings of the 6th International Workshop on Randomization and Approximation Techniques
Approximating concept stability
ICFCA'12 Proceedings of the 10th international conference on Formal Concept Analysis
FUN'12 Proceedings of the 6th international conference on Fun with Algorithms
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Two natural classes of counting problems that are interreducible under approximation-preserving reductions are: (i) those that admit a particular kind of efficient approximation algorithm known as an "FPRAS," and (ii) those that are complete for #P with respect to approximation-preserving reducibility. We describe and investigate not only these two classes but also a third class, of intermediate complexity, that is not known to be identical to (i) or (ii). The third class can be characterised as the hardest problems in a logically defined subclass of #P.