On permutations with limited independence
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Low discrepancy sets yield approximate min-wise independent permutation families
Information Processing Letters
Min-wise independent permutations
Journal of Computer and System Sciences - 30th annual ACM symposium on theory of computing
A small approximately min-wise independent family of hash functions
Journal of Algorithms
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
On the Resemblance and Containment of Documents
SEQUENCES '97 Proceedings of the Compression and Complexity of Sequences 1997
On restricted min-wise independence of permutations
Random Structures & Algorithms
Perturbed identity matrices have high rank: Proof and applications
Combinatorics, Probability and Computing
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A family of permutations of $\cal{F}$ [n] = {1,2,…,n} is (ε,k)-min-wise independent if for every nonempty subset X of at most k elements of [n], and for any x ∈ X, the probability that in a random element π of $\cal{F}$, π(x) is the minimum element of π(X), deviates from 1/∣X∣ by at most ε/∣X∣. This notion can be defined for the uniform case, when the elements of $\cal{F}$ are picked according to a uniform distribution, or for the more general, biased case, in which the elements of $\cal{F}$ are chosen according to a given distribution D. It is known that this notion is a useful tool for indexing replicated documents on the web. We show that even in the more general, biased case, for all admissible k and ε and all large n, the size of $\cal{F}$ must satisfy $$|{\cal{F}}| \ge \Omega \left({k \over \varepsilon^2\log(1/\varepsilon)} \log n\right),$$ as well as $$|{\cal{F}}| \ge \Omega \left({k^2 \over \varepsilon\log(1/\varepsilon)} \log n\right).$$ This improves the best known previous estimates even for the uniform case. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2007