The maximum concurrent flow problem
Journal of the ACM (JACM)
Cut problems and their application to divide-and-conquer
Approximation algorithms for NP-hard problems
Semidefinite programming in combinatorial optimization
Mathematical Programming: Series A and B - Special issue: papers from ismp97, the 16th international symposium on mathematical programming, Lausanne EPFL
Finite metric spaces: combinatorics, geometry and algorithms
Proceedings of the eighteenth annual symposium on Computational geometry
On average distortion of embedding metrics into the line and into L1
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Universal classes of hash functions (Extended Abstract)
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
Journal of Computer and System Sciences - STOC 2001
Euclidean distortion and the sparsest cut
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Noise stability of functions with low in.uences invariance and optimality
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Integrality gaps for sparsest cut and minimum linear arrangement problems
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
ON THE HARDNESS OF APPROXIMATING MULTICUT AND SPARSEST-CUT
Computational Complexity
Expander flows, geometric embeddings and graph partitioning
Journal of the ACM (JACM)
Improved Lower Bounds for Embeddings into $L_1$
SIAM Journal on Computing
Bounded Independence Fools Halfspaces
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
A $(\log n)^{\Omega(1)}$ Integrality Gap for the Sparsest Cut SDP
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
SDP Integrality Gaps with Local ell_1-Embeddability
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Integrality Gaps for Strong SDP Relaxations of UNIQUE GAMES
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Pseudorandom generators for polynomial threshold functions
Proceedings of the forty-second ACM symposium on Theory of computing
Bounded Independence Fools Degree-2 Threshold Functions
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
k-Independent Gaussians Fool Polynomial Threshold Functions
CCC '11 Proceedings of the 2011 IEEE 26th Annual Conference on Computational Complexity
Explicit Construction of a Small $\epsilon$-Net for Linear Threshold Functions
SIAM Journal on Computing
A Small PRG for Polynomial Threshold Functions of Gaussians
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
FOCS '12 Proceedings of the 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science
FOCS '12 Proceedings of the 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science
Locally testable codes and cayley graphs
Proceedings of the 5th conference on Innovations in theoretical computer science
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We give improved pseudorandom generators (PRGs) for Lipschitz functions of low-degree polynomials over the hypercube. These are functions of the form ψ(P(x)), where P:{1,-1}n - R is a low-degree polynomial and ψ:R - R is a function with small Lipschitz constant. PRGs for smooth functions of low-degree polynomials have received a lot of attention recently and play an important role in constructing PRGs for the natural class of polynomial threshold functions [12,13,24,16,15]. In spite of the recent progress, no nontrivial PRGs were known for fooling Lipschitz functions of degree O(log n) polynomials even for constant error rate. In this work, we give the first such generator obtaining a seed-length of (log n)~O(l2/ε2) for fooling degree l polynomials with error ε. Previous generators had an exponential dependence on the degree l. We use our PRG to get better integrality gap instances for sparsest cut, a fundamental problem in graph theory with many applications in graph optimization. We give an instance of uniform sparsest cut for which a powerful semi-definite relaxation (SDP) first introduced by Goemans and Linial and studied in the seminal work of Arora, Rao and Vazirani [3] has an integrality gap of exp(Ω((log log n)1/2)). Understanding the performance of the Goemans-Linial SDP for uniform sparsest cut is an important open problem in approximation algorithms and metric embeddings. Our work gives a near-exponential improvement over previous lower bounds which achieved a gap of Ω(log log n) [11,21]. Our gap instance builds on the recent short code gadgets of Barak et al. [5].