Min-wise Independent Permutations

Min-wise Independent Permutations (1998)

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by Andrei Z. Broder , Moses Charikar , Alan M. Frieze , Michael Mitzenmacher

Venue:	Journal of Computer and System Sciences
Citations:	273 - 11 self

BibTeX

@ARTICLE{Broder98min-wiseindependent,
    author = {Andrei Z. Broder and Moses Charikar and Alan M. Frieze and Michael Mitzenmacher},
    title = {Min-wise Independent Permutations},
    journal = {Journal of Computer and System Sciences},
    year = {1998},
    volume = {60},
    pages = {327--336}
}

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Abstract

We define and study the notion of min-wise independent families of permutations. We say that F ⊆ Sn is min-wise independent if for any set X ⊆ [n] and any x ∈ X, when π is chosen at random in F we have Pr(min{π(X)} = π(x)) = 1 |X |. In other words we require that all the elements of any fixed set X have an equal chance to become the minimum element of the image of X under π. Our research was motivated by the fact that such a family (under some relaxations) is essential to the algorithm used in practice by the AltaVista web index software to detect and filter near-duplicate documents. However, in the course of our investigation we have discovered interesting and challenging theoretical questions related to this concept – we present the solutions to some of them and we list the rest as open problems.

Keyphrases

min-wise independent permutation equal chance challenging theoretical question open problem altavista web index software fixed set min-wise independent family minimum element near-duplicate document