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Min-Wise Independent Linear Permutations
2000
Electronic Journal of Combinatorics
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the point of view of approximate 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. ...
doi:10.37236/1504
fatcat:lv5t6yuyc5ff3fzmnxjfyssrru
Min-Wise Independent Permutations
2000
Journal of computer and system sciences (Print)
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We define and study the notion of 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. ...
doi:10.1006/jcss.1999.1690
fatcat:zj6upydzyza5faywbjpqodfidi
On restricted min-wise independence of permutations
2003
Random structures & algorithms (Print)
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A family of 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. ...
doi:10.1002/rsa.10101
fatcat:tas56hiymvhh3nq7mlzwfjgim4
Completeness and robustness properties of min-wise independent permutations
2000
Random structures & algorithms (Print)
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We provide several new results related to the concept of 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. ...
doi:10.1002/1098-2418(200101)18:1<18::aid-rsa2>3.0.co;2-m
fatcat:xn455o5rsbgv7izzzgbluur65u
Completeness and Robustness Properties of Min-Wise Independent Permutations
[chapter]
1999
Lecture Notes in Computer Science
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We provide several new results related to the concept of 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. ...
doi:10.1007/978-3-540-48413-4_1
fatcat:cn4muc2oznanznwml5tczeoanm
Min-wise independent groups
2003
European journal of combinatorics (Print)
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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 ...
doi:10.1016/s0195-6698(03)00081-7
fatcat:4r343hnjgbcy7gqkrrixrkeyum
Page 1273 of Mathematical Reviews Vol. , Issue 2001B
[page]
2001
Mathematical Reviews
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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.” ...
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
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In this paper, we give a lower bound for the size of k-restricted 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] . ...
doi:10.1145/780542.780645
dblp:conf/stoc/ItohTT03
fatcat:ekcl4vxzdre57ngyehm75d772q
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
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In this paper, we give a lower bound for the size of k-restricted 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] . ...
doi:10.1145/780642.780645
fatcat:jkwzrk6yizcfbfzr6xlxz2otua
On (ɛ,k)-min-wise independent permutations
2007
Random structures & algorithms (Print)
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A family of 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 ...
doi:10.1002/rsa.20184
fatcat:a336czhmpre6bjnp4bvhepwf2y
Derandomized Constructions of k-Wise (Almost) Independent Permutations
[chapter]
2005
Lecture Notes in Computer Science
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For k = 2 the set of 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 ...
doi:10.1007/11538462_30
fatcat:wizwe66lsjckvayhaes4tmpivy
Derandomized Constructions of k-Wise (Almost) Independent Permutations
2008
Algorithmica
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For k = 2 the set of 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 ...
doi:10.1007/s00453-008-9267-y
fatcat:lwrq7pdwt5cebjni4htczgevsu
Page 5013 of Mathematical Reviews Vol. , Issue 2001G
[page]
2001
Mathematical Reviews
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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'. ...
Identifying and Filtering Near-Duplicate Documents
[chapter]
2000
Lecture Notes in Computer Science
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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 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. ...
doi:10.1007/3-540-45123-4_1
fatcat:httjwghysrdvdbvgizaranrynm
Perturbed Identity Matrices Have High Rank: Proof and Applications
2008
Combinatorics, probability & computing
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Nearly 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 ...
doi:10.1017/s0963548307008917
fatcat:s3cvdhpk7zffbmpaztctzun33u
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