A fast parallel algorithm for the maximal independent set problem
Journal of the ACM (JACM)
A fast and simple randomized parallel algorithm for the maximal independent set problem
Journal of Algorithms
A simple parallel algorithm for the maximal independent set problem
SIAM Journal on Computing
On the power of two-point based sampling
Journal of Complexity
Small-bias probability spaces: efficient constructions and applications
SIAM Journal on Computing
Constructing small sample spaces satisfying given constraints
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Self-testing/correcting with applications to numerical problems
Journal of Computer and System Sciences - Special issue: papers from the 22nd ACM symposium on the theory of computing, May 14–16, 1990
On construction of k-wise independent random variables
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
Efficient approximation of product distributions
Random Structures & Algorithms
MODp-tests, almost independence and small probability spaces
Random Structures & Algorithms
Robust Characterizations of Polynomials withApplications to Program Testing
SIAM Journal on Computing
Testing that distributions are close
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Testing Random Variables for Independence and Identity
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Algorithms column: sublinear time algorithms
ACM SIGACT News
Almost k-wise independence versus k-wise independence
Information Processing Letters
Sublinear algorithms for testing monotone and unimodal distributions
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Testing k-wise and almost k-wise independence
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Towards 3-query locally decodable codes of subexponential length
Journal of the ACM (JACM)
Testing for Concise Representations
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Strong Lower Bounds for Approximating Distribution Support Size and the Distinct Elements Problem
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Removing randomness in parallel computation without a processor penalty
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Simple construction of almost k-wise independent random variables
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
Gaussian Bounds for Noise Correlation of Functions and Tight Analysis of Long Codes
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
3-query locally decodable codes of subexponential length
Proceedings of the forty-first annual ACM symposium on Theory of computing
Testing juntas nearly optimally
Proceedings of the forty-first annual ACM symposium on Theory of computing
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
Testing Closeness of Discrete Distributions
Journal of the ACM (JACM)
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A distribution D over Σ1 × ... × Σn is called (non-uniform) k-wise independent if for any set of k indices {i1,..., ik} and for any z1...zk ∈ Σi1×...×Σik, PrX-D[Xi1...Xik = z1 ... zk] = PrX-D[Xi1 = z1] ... PrX-D[Xik = zk]. We study the problem of testing (non-uniform) k-wise independent distributions over product spaces. For the uniform case we show an upper bound on the distance between a distribution D from the set of k-wise independent distributions in terms of the sum of Fourier coefficients of D at vectors of weight at most k. Such a bound was previously known only for the binary field. For the non-uniform case, we give a new characterization of distributions being k-wise independent and further show that such a characterization is robust. These greatly generalize the results of Alon et al. [1] on uniform k-wise independence over the binary field to non-uniform k-wise independence over product spaces. Our results yield natural testing algorithms for k-wise independence with time and sample complexity sublinear in terms of the support size when k is a constant. The main technical tools employed include discrete Fourier transforms and the theory of linear systems of congruences.