Results 1  10
of
181,681
Moments Tensors, Hilbert’s Identity, and kwise Uncorrelated Random Variables
, 2011
"... In this paper we introduce a notion to be called kwise uncorrelated random variables, which is similar but not identical to the socalled kwise independent random variables in the literature. We show how to construct kwise uncorrelated random variables by a simple procedure. The constructed rando ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
In this paper we introduce a notion to be called kwise uncorrelated random variables, which is similar but not identical to the socalled kwise independent random variables in the literature. We show how to construct kwise uncorrelated random variables by a simple procedure. The constructed
Simple Constructions of Almost kwise Independent Random Variables
, 1992
"... We present three alternative simple constructions of small probability spaces on n bits for which any k bits are almost independent. The number of bits used to specify a point in the sample space is (2 + o(1))(log log n + k/2 + log k + log 1 ɛ), where ɛ is the statistical difference between the dist ..."
Abstract

Cited by 319 (42 self)
 Add to MetaCart
We present three alternative simple constructions of small probability spaces on n bits for which any k bits are almost independent. The number of bits used to specify a point in the sample space is (2 + o(1))(log log n + k/2 + log k + log 1 ɛ), where ɛ is the statistical difference between
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
, 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
∈ Σik, PrX∼D[Xi1 · · ·Xik = z1 · · · zk] = PrX∼D[Xi1 = z1] · · ·PrX∼D[Xik = zk]. kwise independent distributions look random “locally ” to an observer of only k coordinates, even though they may be far from random “globally”. Because of this key feature, kwise independent distributions
The space complexity of approximating the frequency moments
 JOURNAL OF COMPUTER AND SYSTEM SCIENCES
, 1996
"... The frequency moments of a sequence containing mi elements of type i, for 1 ≤ i ≤ n, are the numbers Fk = �n i=1 mki. We consider the space complexity of randomized algorithms that approximate the numbers Fk, when the elements of the sequence are given one by one and cannot be stored. Surprisingly, ..."
Abstract

Cited by 855 (12 self)
 Add to MetaCart
The frequency moments of a sequence containing mi elements of type i, for 1 ≤ i ≤ n, are the numbers Fk = �n i=1 mki. We consider the space complexity of randomized algorithms that approximate the numbers Fk, when the elements of the sequence are given one by one and cannot be stored. Surprisingly
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
kwise independent random graphs
 49TH ANNUAL IEEE SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE (FOCS
, 2008
"... We study the kwise independent relaxation of the usual model G(N, p) of random graphs where, as in this model, N labeled vertices are fixed and each edge is drawn with probability p, however, it is only required that the distribution of any subset of k edges is independent. This relaxation can be r ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
We study the kwise independent relaxation of the usual model G(N, p) of random graphs where, as in this model, N labeled vertices are fixed and each edge is drawn with probability p, however, it is only required that the distribution of any subset of k edges is independent. This relaxation can
Factor Graphs and the SumProduct Algorithm
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1998
"... A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple c ..."
Abstract

Cited by 1787 (72 self)
 Add to MetaCart
A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple
Improved Approximation Algorithms for Maximum Cut and Satisfiability Problems Using Semidefinite Programming
 Journal of the ACM
, 1995
"... We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least .87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds the solution ..."
Abstract

Cited by 1231 (13 self)
 Add to MetaCart
We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least .87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds
Results 1  10
of
181,681