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### Min-Wise Independent Linear Permutations

Tom Bohman, Colin Cooper, Alan Frieze
2000 Electronic Journal of Combinatorics
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.  ...

### Min-Wise Independent Permutations

Andrei Z Broder, Moses Charikar, Alan M Frieze, Michael Mitzenmacher
2000 Journal of computer and system sciences (Print)
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.  ...

### On restricted min-wise independence of permutations

Ji?� Matou?ek, Milo? Stojakovi?
2003 Random structures & algorithms (Print)
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.  ...

### Completeness and robustness properties of min-wise independent permutations

Andrei Z. Broder, Michael Mitzenmacher
2000 Random structures & algorithms (Print)
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.  ...

### Completeness and Robustness Properties of Min-Wise Independent Permutations [chapter]

Andrei Z. Broder, Michael Mitzenmacher
1999 Lecture Notes in Computer Science
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.  ...

### Min-wise independent groups

C. Franchi, M. Vsemirnov
2003 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  ...

### 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.”  ...

### On the sample size of k-restricted min-wise independent permutations and other k-wise distributions

Toshiya Itoh, Yoshinori Takei, Jun Tarui
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 min-wise independent permutation family.  ...  An explicit study of min-wise independent permutation families, together with their variants -k-restricted, approximate, et al .  ...  Acknowledgments The authors thank anonymous referees for suggesting them the relevance of their result on k-wise independence to the result of orthogonal arrays  .  ...

### On the sample size of k-restricted min-wise independent permutations and other k-wise distributions

Toshiya Itoh, Yoshinori Takei, Jun Tarui
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 min-wise independent permutation family.  ...  An explicit study of min-wise independent permutation families, together with their variants -k-restricted, approximate, et al .  ...  Acknowledgments The authors thank anonymous referees for suggesting them the relevance of their result on k-wise independence to the result of orthogonal arrays  .  ...

### On (ɛ,k)-min-wise independent permutations

Noga Alon, Toshiya Itoh, Tatsuya Nagatani
2007 Random structures & algorithms (Print)
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  ...

### Derandomized Constructions of k-Wise (Almost) Independent Permutations [chapter]

Eyal Kaplan, Moni Naor, Omer Reingold
2005 Lecture Notes in Computer Science
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  ...

### Derandomized Constructions of k-Wise (Almost) Independent Permutations

Eyal Kaplan, Moni Naor, Omer Reingold
2008 Algorithmica
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  ...

### 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'.  ...

### Identifying and Filtering Near-Duplicate Documents [chapter]

Andrei Z. Broder
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 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.  ...

### Perturbed Identity Matrices Have High Rank: Proof and Applications

NOGA ALON
2008 Combinatorics, probability & computing
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  ...
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