| Abstract: | A family of permutations of  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  , 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  are picked according to a uniform distribution, or for the more general, biased case, in which the elements of  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  must satisfy  as well as  This improves the best known previous estimates even for the uniform case. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2007 |
