How to generate factored random numbers
SIAM Journal on Computing - Special issue on cryptography
Monte-Carlo approximation algorithms for enumeration problems
Journal of Algorithms
SIAM Journal on Computing
Generating random spanning trees more quickly than the cover time
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
A quasi-polynomial-time algorithm for sampling words from a context-free language
Information and Computation
Faster random generation of linear extensions
Discrete Mathematics - Special issue on partial ordered sets
Separating Nondeterministic Time Complexity Classes
Journal of the ACM (JACM)
Simple Markov-chain algorithms for generating bipartite graphs and tournaments
Random Structures & Algorithms
SIAM Journal on Computing
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
Markov Chain Algorithms for Planar Lattice Structures
SIAM Journal on Computing
A Probabilistic-Time Hierarchy Theorem for "Slightly Non-uniform" Algorithms
RANDOM '02 Proceedings of the 6th International Workshop on Randomization and Approximation Techniques
Linear time encodable and list decodable codes
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
A polynomial-time approximation algorithm for the permanent of a matrix with nonnegative entries
Journal of the ACM (JACM)
Hierarchy Theorems for Probabilistic Polynomial Time
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Random Walks on Truncated Cubes and Sampling 0-1 Knapsack Solutions
SIAM Journal on Computing
Hierarchies for semantic classes
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
CCC '07 Proceedings of the Twenty-Second Annual IEEE Conference on Computational Complexity
A Generic Time Hierarchy with One Bit of Advice
Computational Complexity
Foundations and Trends® in Theoretical Computer Science
Sampling stable marriages: why spouse-swapping won't work
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
A hierarchy for nondeterministic time complexity
Journal of Computer and System Sciences
Faster Generation of Random Spanning Trees
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Space Hierarchy Results for Randomized and other Semantic Models
Computational Complexity
Approximately Counting Integral Flows and Cell-Bounded Contingency Tables
SIAM Journal on Computing
On the Implementation of Huge Random Objects
SIAM Journal on Computing
The equivalence of sampling and searching
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
Robust simulations and significant separations
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
From logarithmic advice to single-bit advice
Studies in complexity and cryptography
Extractors for Circuit Sources
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Exact counting of Euler tours for generalized series-parallel graphs
Journal of Discrete Algorithms
Extractors and Lower Bounds for Locally Samplable Sources
ACM Transactions on Computation Theory (TOCT)
The Complexity of Distributions
SIAM Journal on Computing
Bounded-Depth Circuits Cannot Sample Good Codes
Computational Complexity - Selected papers from the 26th Annual IEEE Conference on Computational Complexity (CCC 2011)
Large Deviation Bounds for Decision Trees and Sampling Lower Bounds for AC0-Circuits
FOCS '12 Proceedings of the 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science
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We show that "a little more time gives a lot more power to sampling algorithms." We prove that for every constant k ≥ 2, every polynomial time bound t, and every polynomially small ε, there exists a family of distributions on k elements that can be sampled exactly in polynomial time but cannot be sampled within statistical distance 1-1/k-ε in time t. This implies the following general time hierarchy for sampling distributions on arbitrary-size domains such as {0,1}n: For every polynomial time bound t and every constant ε0, there exists a family of distributions that can be sampled exactly in polynomial time but cannot be sampled within statistical distance 1-ε in time t. Our proof involves reducing the problem to a communication problem over a certain type of noisy channel. To solve the latter problem we use a type of list-decodable code for a setting where there is no bound on the number of errors but each error gives more information than an erasure. This type of code can be constructed using certain known traditional list-decodable codes, but we give a new construction that is elementary, self-contained, and tailored to this setting.