Min-wise independent permutations (extended abstract)
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
On permutations with limited independence
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Non-Interactive Zero-Knowledge: A Low-Randomness Characterization of NP
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
On the sample size of k-restricted min-wise independent permutations and other k-wise distributions
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
A derandomization using min-wise independent permutations
Journal of Discrete Algorithms
Improved range-summable random variable construction algorithms
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms and online mechanisms for item pricing
EC '06 Proceedings of the 7th ACM conference on Electronic commerce
Fast range-summable random variables for efficient aggregate estimation
Proceedings of the 2006 ACM SIGMOD international conference on Management of data
Pseudo-random number generation for sketch-based estimations
ACM Transactions on Database Systems (TODS)
Improved Approximation Algorithms for Item Pricing with Bounded Degree and Valuation
IEICE - Transactions on Information and Systems
Smooth entropy and Rényi entropy
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
Simple and tight bounds for information reconciliation and privacy amplification
ASIACRYPT'05 Proceedings of the 11th international conference on Theory and Application of Cryptology and Information Security
Randomized approximations of parameterized counting problems
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Pseudorandom generators from one-way functions: a simple construction for any hardness
TCC'06 Proceedings of the Third conference on Theory of Cryptography
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This set of notes gives several applications of the following paradigm. The paradigm consists of two complementary parts. The first part is to design a probabilistic algorithm described by a sequence of random variables so that the analysis is valid assuming limited independence between the random variables. The second part is the design of a small probability space for the random variables such that they are somewhat independent of each other. Thus, the analysis of the algorithm holds even when the random variables used by the algorithm are generated according to the small space.