Results 1  10
of
192,525
Almost kwise vs. kwise independent . . .
, 2013
"... A family of permutations in Sn is kwise independent if a uniform permutation chosen from the family maps any sequence of k distinct elements to any sequence of k distinct elements with equal probability. Efficient constructions of kwise independent permutations are known for k = 2 and k = 3 base ..."
Abstract
 Add to MetaCart
A family of permutations in Sn is kwise independent if a uniform permutation chosen from the family maps any sequence of k distinct elements to any sequence of k distinct elements with equal probability. Efficient constructions of kwise independent permutations are known for k = 2 and k = 3
Testing kwise and almost kwise independence
 In 39th Annual ACM Symposium on Theory of Computing
, 2007
"... In this work, we consider the problems of testing whether a distribution over {0, 1} n is kwise (resp. (ɛ, k)wise) independent using samples drawn from that distribution. For the problem of distinguishing kwise independent distributions from those that are δfar from kwise independence in statis ..."
Abstract

Cited by 30 (10 self)
 Add to MetaCart
in statistical distance, we upper bound the number of required samples by Õ(nk /δ 2) and lower bound it by Ω(n k−1 2 /δ) (these bounds hold for constant k, and essentially the same bounds hold for general k). To achieve these bounds, we use Fourier analysis to relate a distribution’s distance from kwise
Derandomized constructions of kwise (almost) independent permutations
 In Proceedings of the 9th Workshop on Randomization and Computation (RANDOM
, 2005
"... Abstract Constructions of kwise almost independent permutations have been receiving a growingamount of attention in recent years. However, unlike the case of kwise independent functions,the size of previously constructed families of such permutations is far from optimal. This paper gives a new met ..."
Abstract

Cited by 24 (4 self)
 Add to MetaCart
such generator is implied by Reingold's logspace algorithm for undirected connectivity [35, 36]. We obtain families of kwise almost independent permutations, with anoptimal description length, up to a constant factor. More precisely, if the distance from uniform for any k tuple should be at most ffi
Testing kwise
, 2012
"... A probability distribution over {0, 1}n is kwise independent if its restriction to any k coordinates is uniform. More generally, a discrete distribution D over Σ1 × · · · × Σn is called (nonuniform) kwise independent if for any subset of k indices {i1,..., ik} and for any z1 ∈ Σi1,..., zk ∈ Σ ..."
Abstract
 Add to MetaCart
A probability distribution over {0, 1}n is kwise independent if its restriction to any k coordinates is uniform. More generally, a discrete distribution D over Σ1 × · · · × Σn is called (nonuniform) kwise independent if for any subset of k indices {i1,..., ik} and for any z1 ∈ Σi1,..., zk
On kwise independent distributions and Boolean functions
"... We pursue a systematic study of the following problem. Let f: {0, 1} n → {0, 1} be a (usually monotone) boolean function whose behaviour is well understood when the input bits are identically independently distributed. What can be said about the behaviour of the function when the input bits are not ..."
Abstract

Cited by 9 (1 self)
 Add to MetaCart
the extremal properties of kwise independent distributions and provide ways of constructing such distributions. These constructions are connected to linear error correcting codes. We also utilize duality theory and show that for the function f to behave (almost) the same under all kwise independent inputs
Testing Nonuniform kwise Independent Distributions over Product Spaces
"... A discrete distribution D over Σ1 × · · · × Σn is called (nonuniform) kwise independent if for any set of k indexes {i1,..., ik} and for any z1 ∈ Σi1,..., zk ∈ Σik, PrX∼D[Xi1 · · · Xik = z1 · · · zk] = PrX∼D[Xi1 = z1] · · · PrX∼D[Xik = zk]. We study the problem of testing (nonuniform) ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
when the underlying domain is {0, 1} n. For the nonuniform case, we give a new characterization of distributions being kwise independent and further show that such a characterization is robust based on our results for the uniform case. These greatly generalize the results of Alon et al. [1
Domain kWise Consistency Made as Simple as Generalized Arc Consistency
"... Abstract. In Constraint Programming (CP), Generalized Arc Consistency (GAC) is the central property used for making inferences when solving Constraint Satisfaction Problems (CSPs). Developing simple and practical filtering algorithms based on consistencies stronger than GAC is a challenge for the CP ..."
Abstract
 Add to MetaCart
for the CP community. In this paper, we propose to combine kWise Consistency (kWC) with GAC, where kWC states that every tuple in a constraint can be extended to every set of k − 1 additional constraints. Our contribution is as follows. First, we derive a domainfiltering consistency, called Domain kWise
Robust characterizations of kwise independence over product spaces and related testing results. Random Structures and Algorithms
, 2012
"... A discrete distribution D over Σ1 × · · · × Σn is called (nonuniform) kwise independent if for any subset of k indices {i1,..., ik} and for any z1 ∈ Σi1,..., zk ∈ Σik, PrX∼D[Xi1 · · ·Xik = z1 · · · zk] = PrX∼D[Xi1 = z1] · · ·PrX∼D[Xik = zk]. We study the problem of testing (nonuniform) k ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
when the underlying domain is {0, 1}n. For the nonuniform case, we give a new characterization of distributions being kwise independent and further show that such a characterization is robust based on our results for the uniform case. These results greatly generalize those of Alon et al. [STOC’07, pp
Results 1  10
of
192,525