A fast and simple randomized parallel algorithm for the maximal independent set problem
Journal of Algorithms
Constructing Small Sample Spaces Satisfying Given Constants
SIAM Journal on Discrete Mathematics
Limits and rates of convergence for the distribution of search cost under the move-to-front rule
Theoretical Computer Science
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
Completeness and robustness properties of min-wise independent permutations
Random Structures & 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 (ε,k)-min-wise independent 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 F ⊆ Sn, with a probability distribution on it is called k-restricted rain-wise independent if we have Pr[min π(X) = π(x)] = 1|X| for every subset X ⊆ [n] with |X| ≤ k, every x ∈ X, and π ∈ F chosen at random. We present a simple proof of a result of Norin: every such family has size at least (n-1 k-1/2) . Some features of our method might be of independent interest. The best available upper bound for the size of such family is 1 + σj=2k(J - 1) (n j). We show that this bound is tight if the goal is to imitate not the uniform distribution on Sn, but a distribution given by assigning suitable priorities to the elements of [n] (the stationary distribution of the Tsetlin library, or self-organizing lists). This is analogous to a result of Karloff and Mansour for k-wise independent random variables. We also investigate the cases where the min-wise independence condition is required only for sets X of size exactly k (where we have only an ω(log log n + k) lower bound), or for sets of size k and k - 1 (where we already obtain a lower bound of n - k + 2).