Min-wise independent groups

Authors:
C. Franchi;M. Vsemirnov
Affiliations:
Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore, via Musei 41, 25121 Brescia, Italy;Sidney Sussex College, Sidney Street, Cambridge CB2 3HU, UK
Venue:
European Journal of Combinatorics
Year:
2003

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Min-wise independent permutations

Journal of Computer and System Sciences - 30th annual ACM symposium on theory of computing
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

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Abstract

Let Ω be a finite set of cardinality n with a linear order on it and let k be a positive integer. Let F be a set of permutations on Ω and let PrF be an arbitrary distribution of probability on F The set F is said to be biased k-restricted min-wise independent if for every subset X of Ω such that |X| ≤ k, and every x ∈ X, when π is chosen at random in F, we have that PrF(min π(X) = π(x)) = /1|X|;. We study biased k-restricted min-wise independent groups. In particular, we prove that when k is close to n, then biased k-restricted min-wise independent groups are transitive.