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Min-Wise Independent Linear Permutations

2000
*
Electronic Journal of Combinatorics
*

the point of view of approximate

doi:10.37236/1504
fatcat:lv5t6yuyc5ff3fzmnxjfyssrru
*min*-*wise**independence*. ... A set of*permutations*${\cal F} \subseteq S_n$ is*min*-*wise**independent*if for any set $X \subseteq [n]$ and any $x \in X$, when $\pi$ is chosen at random in ${\cal F}$ we have ${\bf P} \left(\*min*\{\pi( ... Thus a simply chosen random*linear**permutation*will suffice for an average set from the point of view of*min*-*wise**independence*. ...##
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Min-Wise Independent Permutations

2000
*
Journal of computer and system sciences (Print)
*

We define and study the notion of

doi:10.1006/jcss.1999.1690
fatcat:zj6upydzyza5faywbjpqodfidi
*min*-*wise**independent*families of*permutations*. ... We say that F ⊆ S n is*min*-*wise**independent*if for any set X ⊆ [n] and any x ∈ X, when π is chosen at random in F we have In other words we require that all the elements of any fixed set X have an equal ... In this sense,*linear*transformations are approximately*min*-*wise**independent*with respect to random sets. ...##
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On restricted min-wise independence of permutations

2003
*
Random structures & algorithms (Print)
*

A family of

doi:10.1002/rsa.10101
fatcat:tas56hiymvhh3nq7mlzwfjgim4
*permutations*F ⊆ S n with a probability distribution on it is called k-restricted*min*-*wise**independent*if we have Pr[*min*π(X) = π(x)] = ... The investigation of k-*wise**independence*predates the study of*min*-*wise**independent**permutations*(and most of the questions, results, and techniques concerning*min*-*wise**independence*have their analogs ... j ( n j ) (= Θ(n k ) for k fixed) for biased k-restricted*min*-*wise**independent*families follows by the*linear*programming approach. ...##
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Completeness and robustness properties of min-wise independent permutations

2000
*
Random structures & algorithms (Print)
*

We provide several new results related to the concept of

doi:10.1002/1098-2418(200101)18:1<18::aid-rsa2>3.0.co;2-m
fatcat:xn455o5rsbgv7izzzgbluur65u
*min*-*wise**independence*. ... A surprising result arising from our consideration of robustness is that under a random*permutation*from a*min*-*wise**independent*family, any element of a fixed set has an equal chance to get any rank in ... our main result can be extended to approximate*min*-*wise**independent**permutation*families. ...##
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Completeness and Robustness Properties of Min-Wise Independent Permutations
[chapter]

1999
*
Lecture Notes in Computer Science
*

We provide several new results related to the concept of

doi:10.1007/978-3-540-48413-4_1
fatcat:cn4muc2oznanznwml5tczeoanm
*min*-*wise**independence*. ... A surprising result arising from our consideration of robustness is that under a random*permutation*from a*min*-*wise**independent*family, any element of a fixed set has an equal chance to get any rank in ... our main result can be extended to approximate*min*-*wise**independent**permutation*families. ...##
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Min-wise independent groups

2003
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European journal of combinatorics (Print)
*

*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. ...

*Min*-

*wise*

*independence*with respect to every

*linear*order In this section we consider groups of

*permutations*on the set Ω that are 2-restricted

*min*-

*wise*

*independent*with respect to any

*linear*order on Ω ...

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Page 1273 of Mathematical Reviews Vol. , Issue 2001B
[page]

2001
*
Mathematical Reviews
*

likely (note that n-restricted

*min*-*wise**independence*is referred to simply as*min*-*wise*indepen- dence). ... ,---,1) = e"-° for families @ of*min*-*wise**independent**permutations*on {0,1,---, — 1}, which achieves the known lower bound.” ...##
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On the sample size of k-restricted min-wise independent permutations and other k-wise distributions

2003
*
Proceedings of the thirty-fifth ACM symposium on Theory of computing - STOC '03
*

In this paper, we give a lower bound for the size of k-restricted

doi:10.1145/780542.780645
dblp:conf/stoc/ItohTT03
fatcat:ekcl4vxzdre57ngyehm75d772q
*min*-*wise**independent**permutation*family. ... An explicit study of*min*-*wise**independent**permutation*families, together with their variants -k-restricted, approximate, et al [4]. ... Acknowledgments The authors thank anonymous referees for suggesting them the relevance of their result on k-*wise**independence*to the result of orthogonal arrays [16] . ...##
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On the sample size of k-restricted min-wise independent permutations and other k-wise distributions

2003
*
Proceedings of the thirty-fifth ACM symposium on Theory of computing - STOC '03
*

In this paper, we give a lower bound for the size of k-restricted

doi:10.1145/780642.780645
fatcat:jkwzrk6yizcfbfzr6xlxz2otua
*min*-*wise**independent**permutation*family. ... An explicit study of*min*-*wise**independent**permutation*families, together with their variants -k-restricted, approximate, et al [4]. ... Acknowledgments The authors thank anonymous referees for suggesting them the relevance of their result on k-*wise**independence*to the result of orthogonal arrays [16] . ...##
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On (ɛ,k)-min-wise independent permutations

2007
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Random structures & algorithms (Print)
*

A family of

doi:10.1002/rsa.20184
fatcat:a336czhmpre6bjnp4bvhepwf2y
*permutations*F of [n] = {1, 2, . ... )-*min*-*wise**independent**permutations*. ... Introduction Background A family F of*permutations*of [n] = {1, 2, . . . , n} is an ε-approximate k-restricted*min*-*wise**independent*family (or an (ε, k)-*min*-*wise**independent*family, for short) if for ...##
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Derandomized Constructions of k-Wise (Almost) Independent Permutations
[chapter]

2005
*
Lecture Notes in Computer Science
*

For k = 2 the set of

doi:10.1007/11538462_30
fatcat:wizwe66lsjckvayhaes4tmpivy
*linear**permutations*(ax + b where a = 0) over GF [2 n ] constitutes such a family. ... For k > 3 no explicit (non-trivial) construction is known for k-*wise*exactly*independent**permutations*. ... Informally, a*permutation*family is k-restricted*min*-*wise**independent*(or simply*min*-*wise**independent*, if k = n), if for every distinct k elements, each element is mapped to the minimum among the images ...##
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Derandomized Constructions of k-Wise (Almost) Independent Permutations

2008
*
Algorithmica
*

For k = 2 the set of

doi:10.1007/s00453-008-9267-y
fatcat:lwrq7pdwt5cebjni4htczgevsu
*linear**permutations*(ax + b where a = 0) over GF [2 n ] constitutes such a family. ... For k > 3 no explicit (non-trivial) construction is known for k-*wise*exactly*independent**permutations*. ... Informally, a*permutation*family is k-restricted*min*-*wise**independent*(or simply*min*-*wise**independent*, if k = n), if for every distinct k elements, each element is mapped to the minimum among the images ...##
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Page 5013 of Mathematical Reviews Vol. , Issue 2001G
[page]

2001
*
Mathematical Reviews
*

A

*min*-*wise**independent*set of*permutations*must have at least e”~°) elements, and families with 4” elements exist. Any k-restricted*min*-*wise**independent*family must have Q(k2*/? ... The authors were led by practical applications to the notion of a set of*permutations*¥ C S,, being*min*-*wise**independent*: for any set X C [n], and any x € X, we have Pr(*min*{x(X)} =2(x)) =|X|7'. ...##
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Identifying and Filtering Near-Duplicate Documents
[chapter]

2000
*
Lecture Notes in Computer Science
*

The process of estimating the relative size of intersection of sets and the threshold test discussed above can be applied to arbitrary sets, and thus might be of

doi:10.1007/3-540-45123-4_1
fatcat:httjwghysrdvdbvgizaranrynm
*independent*interest. ... has two aspects: first, resemblance is expressed as a set (of strings) intersection problem, and second, the relative size of intersections is evaluated by a process of random sampling that can be done*independently*... In turns out that to achieve the desired result, the*permutation*must be drawn from a*min*-*wise**independent*family of*permutations*. ...##
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Perturbed Identity Matrices Have High Rank: Proof and Applications

2008
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Combinatorics, probability & computing
*

Nearly

doi:10.1017/s0963548307008917
fatcat:s3cvdhpk7zffbmpaztctzun33u
*min*-*wise**independent**permutations*A family F of*permutations*of [n] = {1, 2, . . . , n} is an ε-approximate k-restricted*min*-*wise**independent*family (or an (ε, k)-*min*-*wise**independent*family, for ...*Min*-*wise**independence*for sets of size exactly k Call a family of*permutations*F of [n], with a distribution D, exactly k*min*-*wise**independent*if for every subset X of exactly k elements of [n] and every ...
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