Approximate counting, uniform generation and rapidly mixing Markov chains
Information and Computation
On sampling with Markov chains
Proceedings of the seventh international conference on Random structures and algorithms
Random Structures & Algorithms
Random generation of 2 × n contingency tables
Random Structures & Algorithms
Polynomial-time counting and sampling of two-rowed contingency tables
Theoretical Computer Science
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Rapidly Mixing Markov Chains for Sampling Contingency Tables with a Constant Number of Rows
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Improved Bounds for Sampling Contingency Tables
RANDOM-APPROX '99 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization Problems: Randomization, Approximation, and Combinatorial Algorithms and Techniques
Random Walks on Truncated Cubes and Sampling 0-1 Knapsack Solutions
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Random walks in convex sets
Approximately counting integral flows and cell-bounded contingency tables
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Assessing data mining results via swap randomization
Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
Every Linear Threshold Function has a Low-Weight Approximator
Computational Complexity
Assessing data mining results via swap randomization
ACM Transactions on Knowledge Discovery from Data (TKDD)
Fully polynomial time approximation schemes for stochastic dynamic programs
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Mathematics of Operations Research
On the Diaconis-Gangolli Markov Chain for Sampling Contingency Tables with Cell-Bounded Entries
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
Faster Algorithms for Sampling and Counting Biological Sequences
SPIRE '09 Proceedings of the 16th International Symposium on String Processing and Information Retrieval
An invariance principle for polytopes
Proceedings of the forty-second ACM symposium on Theory of computing
On the hardness of counting and sampling center strings
SPIRE'10 Proceedings of the 17th international conference on String processing and information retrieval
Approximately Counting Integral Flows and Cell-Bounded Contingency Tables
SIAM Journal on Computing
On the Diaconis-Gangolli Markov chain for sampling contingency tables with cell-bounded entries
Journal of Combinatorial Optimization
On the effective enumerability of NP problems
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
A Deterministic Polynomial-Time Approximation Scheme for Counting Knapsack Solutions
SIAM Journal on Computing
An invariance principle for polytopes
Journal of the ACM (JACM)
On the Hardness of Counting and Sampling Center Strings
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Parameterized top-K algorithms
Theoretical Computer Science
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We give efficient algorithms to sample uniformly, and count approximately, the solutions to a zero-one knapsack problem. The algorithm is based on using dynamic programming to provide a deterministic relative approximation. Then "dart throwing" techniques are used to give arbitrary approximation ratios. We also indicate how further improvements can be obtained using randomized rounding. We extend the approach to several related problems: the m-constraint zero-one knapsack, the general integer knapsack (including its m-constraint version) and contingency tables with constantly many rows.