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On restricted min-wise independence of permutations

2003
*
Random structures & algorithms (Print)
*

A family

doi:10.1002/rsa.10101
fatcat:tas56hiymvhh3nq7mlzwfjgim4
*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)] = ... Acknowledgment We would like to thank Emo Welzl for bringing the problems studied in this paper to our attention, formulating*one**of*them, and for numerous discussions and valuable suggestions. ... Can*one*improve the lower (or upper) bound for {k}-*restricted**min*-*wise**independent*families? ...##
###
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
*

We show that if a family F

doi:10.1145/780542.780645
dblp:conf/stoc/ItohTT03
fatcat:ekcl4vxzdre57ngyehm75d772q
*of**permutations**on*[0, n−1] is k-*restricted**min*-*wise**independent*, then |F | ≥ m(n − 1, k − 1), where m(n, d) = ... In this paper, we give a lower bound for the size*of*k-*restricted**min*-*wise**independent**permutation*family. ... 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] . ...##
###
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
*

We show that if a family F

doi:10.1145/780642.780645
fatcat:jkwzrk6yizcfbfzr6xlxz2otua
*of**permutations**on*[0, n−1] is k-*restricted**min*-*wise**independent*, then |F | ≥ m(n − 1, k − 1), where m(n, d) = ... In this paper, we give a lower bound for the size*of*k-*restricted**min*-*wise**independent**permutation*family. ... 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] . ...##
###
Min-wise independent groups

2003
*
European journal of combinatorics (Print)
*

*min*-

*wise*

*independent*groups. ... 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 We study biased k-

*restricted*... The second author was supported in part by the Cariplo Foundation (Italy) and by grant No 001

*of*the 6th Competition

*of*Young Scientists' Research Projects from the Russian Academy

*of*Sciences. ...

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

2001
*
Mathematical Reviews
*

for families @

*of*k-*restricted**min*-*wise*and k-rankwise*independent**permutations**on*{0,1,---,2—1}, respectively; (2) for upper bounds, ||@|| < n!' ... likely (note that n-*restricted**min*-*wise**independence*is referred to simply as*min*-*wise*indepen- dence). ...##
###
Min-Wise Independent Permutations

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

We define and study the notion

doi:10.1006/jcss.1999.1690
fatcat:zj6upydzyza5faywbjpqodfidi
*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 ... Approx*min*-*wise*,*restricted*, biased distrib*on*F ? ...##
###
On (ɛ,k)-min-wise independent permutations

2007
*
Random structures & algorithms (Print)
*

A family

doi:10.1002/rsa.20184
fatcat:a336czhmpre6bjnp4bvhepwf2y
*of**permutations*F*of*[n] = {1, 2, . ... Acknowledgment: We would like to thank Yoshinori Takei for his valuable comments and for insightful discussions*on*an earlier version*of*the paper. ... The notion*of*(ε, k)-*min*-*wise**independent*families, as well as the related*ones**of*k-*restricted**min*-*wise**independent*families (corresponding to the case ε = 0),*min*-*wise**independent*families (corresponding ...##
###
A derandomization using min-wise independent permutations

2003
*
Journal of Discrete Algorithms
*

*Min*-

*wise*

*independence*is a recently introduced notion

*of*limited

*independence*, similar in spirit to pairwise

*independence*. The latter has proven essential for the derandomization

*of*many algorithms. ... The multi-cover case leads us to discuss the concept

*of*k-minima-

*wise*

*independence*, a natural counterpart to k-

*wise*

*independence*. ...

*Min*-

*wise*

*independence*We provide the necessary definitions for

*min*-

*wise*

*independence*, based

*on*[4] . Let S n be the set

*of*all

*permutations*

*of*[n]. ...

##
###
A Derandomization Using Min-Wise Independent Permutations
[chapter]

1998
*
Lecture Notes in Computer Science
*

*Min*-

*wise*

*independence*is a recently introduced notion

*of*limited

*independence*, similar in spirit to pairwise

*independence*. The latter has proven essential for the derandomization

*of*many algorithms. ... The multi-cover case leads us to discuss the concept

*of*k-minima-

*wise*

*independence*, a natural counterpart to k-

*wise*

*independence*. ...

*Min*-

*wise*

*independence*We provide the necessary definitions for

*min*-

*wise*

*independence*, based

*on*[4] . Let S n be the set

*of*all

*permutations*

*of*[n]. ...

##
###
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*/? ... log(n/k)) elements, but there exists a family (no*restrictions*) with only n2"~' elements which is*min*-*wise**independent*, provided a non-uniform distribution*on*F is allowed. ...##
###
Geometric representation of 3-restricted min-wise independent sets of permutations
[article]

2015
*
arXiv
*
pre-print

We study properties

arXiv:1512.07911v1
fatcat:bhvkltqgmbagfnqykhxel7zi3m
*of*3-*restricted**min*-*wise**independent*sets*of**permutations*and prove that the class*of*these sets is isomorphic to the class*of*subsets*of*vertices*of*multi-dimentional hypercube*of*... certain size with certain pair-*wise*distances fixed. ... [1] A set*of**permutations*S ⊂ S n is called 3-*restricted**min*-*wise*-*independent*(3-mwi) if ∀X ⊂ [n] : |X| ≤ 3 and ∀x ∈ X #{π ∈ S : π(x) =*min*(π(X))} = |S| |X| . ...##
###
Derandomized Constructions of k-Wise (Almost) Independent Permutations
[chapter]

2005
*
Lecture Notes in Computer Science
*

*On*

*one*hand, some constructions

*of*pseudorandom

*permutations*, and most notably the Luby-Rackoff construction [20] , imply explicit constructions

*of*k-

*wise*almost

*independent*

*permutations*[26] (see references ...

*One*motivation for this study is the relation between k-

*wise*

*independent*

*permutations*and block ciphers [14, 26] . ... Acknowledgments The authors are grateful to Ronen Shaltiel for his invaluable collaboration during the early stages

*of*this work, and thank Danny Harnik, Asaf Nussboim and Adam Smith for useful comments ...

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

2008
*
Algorithmica
*

*On*

*one*hand, some constructions

*of*pseudorandom

*permutations*, and most notably the Luby-Rackoff construction [20] , imply explicit constructions

*of*k-

*wise*almost

*independent*

*permutations*[26] (see references ...

*One*motivation for this study is the relation between k-

*wise*

*independent*

*permutations*and block ciphers [14, 26] . ... Acknowledgments The authors are grateful to Ronen Shaltiel for his invaluable collaboration during the early stages

*of*this work, and thank Danny Harnik, Asaf Nussboim and Adam Smith for useful comments ...

##
###
Simple permutations mix well

2005
*
Theoretical Computer Science
*

We improve

doi:10.1016/j.tcs.2005.09.016
fatcat:pv5xeyuqanfp7cd6iymqbyckby
*on*a result*of*Gowers [An almost m-*wise**independent*random*permutation**of*the cube, Combin. Probab. ... Specifically, we ask what is the number*of*compositions needed to achieve a*permutation*that is close to k-*wise**independent*. ... The new result shows that it suffices to compose*min*( O(n 2 k 2 ), O(n 3 k 2 )) simple*permutations*from F 2 to get close to a k-*wise**independent**permutation*. ...##
###
Simple Permutations Mix Well
[chapter]

2004
*
Lecture Notes in Computer Science
*

Specifically we ask what is the number

doi:10.1007/978-3-540-27836-8_65
fatcat:dndbcbikfzcjlmsckxsd4osazy
*of*compositions needed to achieve a*permutation*that is close to k-*wise**independent*. ... We study the random composition*of*a small family*of*O(n 3 ) simple*permutations**on*{0, 1} n . ... The new result shows that it suffices to compose*min*( O (n 2 k 2 ), O(n 3 k 2 )) simple*permutations*from F 2 to get close to a k-*wise**independent**permutation*. ...
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