Explicit construction of exponential sized families of K-independent sets
Discrete Mathematics
Sparse Approximate Solutions to Linear Systems
SIAM Journal on Computing
Randomized algorithms
Theoretical Computer Science
Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Adaptive Versus Nonadaptive Attribute-Efficient Learning
Machine Learning
Almost Independent and Weakly Biased Arrays: Efficient Constructions and Cryptologic Applications
CRYPTO '00 Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology
The Lovász Local Lemma and Its Applications to some Combinatorial Arrays
Designs, Codes and Cryptography
One sketch for all: fast algorithms for compressed sensing
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
The density algorithm for pairwise interaction testing: Research Articles
Software Testing, Verification & Reliability
On generalized separating hash families
Journal of Combinatorial Theory Series A
Deterministic constructions of compressed sensing matrices
Journal of Complexity
A bound on the size of separating hash families
Journal of Combinatorial Theory Series A
A density-based greedy algorithm for higher strength covering arrays
Software Testing, Verification & Reliability
Efficient and robust compressed sensing using optimized expander graphs
IEEE Transactions on Information Theory
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
Combinatorial Sublinear-Time Fourier Algorithms
Foundations of Computational Mathematics
Deterministic algorithms for the Lovász Local Lemma
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
A survey of combinatorial testing
ACM Computing Surveys (CSUR)
Bounds for separating hash families
Journal of Combinatorial Theory Series A
Combinatorial algorithms for compressed sensing
SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
Efficient conditional expectation algorithms for constructing hash families
IWOCA'11 Proceedings of the 22nd international conference on Combinatorial Algorithms
On greedy algorithms in coding theory
IEEE Transactions on Information Theory - Part 1
Uncertainty principles and ideal atomic decomposition
IEEE Transactions on Information Theory
A generalized uncertainty principle and sparse representation in pairs of bases
IEEE Transactions on Information Theory
Sparse representations in unions of bases
IEEE Transactions on Information Theory
On sparse representations in arbitrary redundant bases
IEEE Transactions on Information Theory
Recovery of short, complex linear combinations via ℓ1 minimization
IEEE Transactions on Information Theory
Recovery of exact sparse representations in the presence of bounded noise
IEEE Transactions on Information Theory
Decoding by linear programming
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
IEEE Transactions on Information Theory
Post-optimization: necessity analysis for combinatorial arrays
Post-optimization: necessity analysis for combinatorial arrays
Randomized post-optimization for t-restrictions
Information Theory, Combinatorics, and Search Theory
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The deterministic construction of measurement matrices for compressive sensing is a challenging problem, for which a number of combinatorial techniques have been developed. One of them employs a widely used column replacement technique based on hash families. It is effective at producing larger measurement matrices from smaller ones, but it can only preserve the strength (level of sparsity supported), not increase it. Column replacement is extended here to produce measurement matrices with larger strength from ingredient arrays with smaller strength. To do this, a new type of hash family, called a strengthening hash family, is introduced. Using these hash families, column replacement is shown to increase strength under two standard notions of recoverability. Then techniques to construct strengthening hash families, both probabilistically and deterministically, are developed. Using a variant of the Stein-Lovasz-Johnson theorem, a deterministic, polynomial time algorithm for constructing a strengthening hash family of fixed strength is derived.