Storing a Sparse Table with 0(1) Worst Case Access Time
Journal of the ACM (JACM)
The analysis of closed hashing under limited randomness
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Approximations of general independent distributions
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Small-bias probability spaces: efficient constructions and applications
SIAM Journal on Computing
Computational geometry: a retrospective
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Computational Complexity
On linear-time deterministic algorithms for optimization problems in fixed dimension
Journal of Algorithms
SIAM Journal on Computing
Algorithmic derandomization via complexity theory
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Derandomized dimensionality reduction with applications
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Lectures on Discrete Geometry
Algorithms with large domination ratio
Journal of Algorithms
Every Linear Threshold Function has a Low-Weight Approximator
CCC '06 Proceedings of the 21st Annual IEEE Conference on Computational Complexity
Uncertainty principles, extractors, and explicit embeddings of l2 into l1
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Almost Euclidean subspaces of ℓN1 via expander codes
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Weak ε-nets and interval chains
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
The Sum of d Small-Bias Generators Fools Polynomials of Degree d
CCC '08 Proceedings of the 2008 IEEE 23rd Annual Conference on Computational Complexity
Euclidean Sections of $\ell_1^N$ with Sublinear Randomness and Error-Correction over the Reals
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Explicit construction of a small epsilon-net for linear threshold functions
Proceedings of the forty-first annual ACM symposium on Theory of computing
Concentration of Measure for the Analysis of Randomized Algorithms
Concentration of Measure for the Analysis of Randomized Algorithms
Pseudorandom generators for polynomial threshold functions
Proceedings of the forty-second ACM symposium on Theory of computing
Bounded Independence Fools Halfspaces
SIAM Journal on Computing
IEEE Transactions on Information Theory
Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
IEEE Transactions on Information Theory
Pseudorandom generators for combinatorial shapes
Proceedings of the forty-third annual ACM symposium on Theory of computing
Explicit Dimension Reduction and Its Applications
SIAM Journal on Computing
A PRG for lipschitz functions of polynomials with applications to sparsest cut
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Improved Approximation of Linear Threshold Functions
Computational Complexity
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We give explicit constructions of $\epsilon$-nets for linear threshold functions on the binary cube and on the unit sphere. The size of the constructed nets is polynomial in the dimension $n$ and in $\frac{1}{\epsilon}$. To the best of our knowledge no such constructions were previously known. Our results match, up to the exponent of the polynomial, the bounds that are achieved by probabilistic arguments. As a corollary we also construct subsets of the binary cube that have size polynomial in $n$ and a covering radius of $\frac{n}{2}-c\sqrt{n\log n}$ for any constant $c$. This improves upon the well-known construction of dual BCH codes that guarantee only a covering radius of $\frac{n}{2}-c\sqrt{n}$.