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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)] =  ...  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?  ... 
doi:10.1002/rsa.10101 fatcat:tas56hiymvhh3nq7mlzwfjgim4

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  
We show that if a family F 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] .  ... 
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

Toshiya Itoh, Yoshinori Takei, Jun Tarui
2003 Proceedings of the thirty-fifth ACM symposium on Theory of computing - STOC '03  
We show that if a family F 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] .  ... 
doi:10.1145/780642.780645 fatcat:jkwzrk6yizcfbfzr6xlxz2otua

Min-wise independent groups

C. Franchi, M. Vsemirnov
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.  ... 
doi:10.1016/s0195-6698(03)00081-7 fatcat:4r343hnjgbcy7gqkrrixrkeyum

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

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  ...  Approx min-wise, restricted, biased distrib on F ?  ... 
doi:10.1006/jcss.1999.1690 fatcat:zj6upydzyza5faywbjpqodfidi

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, .  ...  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  ... 
doi:10.1002/rsa.20184 fatcat:a336czhmpre6bjnp4bvhepwf2y

A derandomization using min-wise independent permutations

Andrei Z. Broder, Moses Charikar, Michael Mitzenmacher
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].  ... 
doi:10.1016/s1570-8667(03)00003-0 fatcat:becsochuanan3bdbtud5yd2mzm

A Derandomization Using Min-Wise Independent Permutations [chapter]

Andrei Z. Broder, Moses Charikar, Michael Mitzenmacher
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].  ... 
doi:10.1007/3-540-49543-6_2 fatcat:kfgmzficsbbv5ft67nlpyij7rq

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]

Victor Bargachev
2015 arXiv   pre-print
We study properties 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| .  ... 
arXiv:1512.07911v1 fatcat:bhvkltqgmbagfnqykhxel7zi3m

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

Eyal Kaplan, Moni Naor, Omer Reingold
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  ... 
doi:10.1007/11538462_30 fatcat:wizwe66lsjckvayhaes4tmpivy

Derandomized Constructions of k-Wise (Almost) Independent Permutations

Eyal Kaplan, Moni Naor, Omer Reingold
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  ... 
doi:10.1007/s00453-008-9267-y fatcat:lwrq7pdwt5cebjni4htczgevsu

Simple permutations mix well

Shlomo Hoory, Avner Magen, Steven Myers, Charles Rackoff
2005 Theoretical Computer Science  
We improve 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.  ... 
doi:10.1016/j.tcs.2005.09.016 fatcat:pv5xeyuqanfp7cd6iymqbyckby

Simple Permutations Mix Well [chapter]

Shlomo Hoory, Avner Magen, Steven Myers, Charles Rackoff
2004 Lecture Notes in Computer Science  
Specifically we ask what is the number 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.  ... 
doi:10.1007/978-3-540-27836-8_65 fatcat:dndbcbikfzcjlmsckxsd4osazy
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