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Detecting high log-densities: an O(n¼) approximation for densest k-subgraph
TLDR
In the Densest k-Subgraph problem, given a graph G and a parameter k, one needs to find a subgraph of G induced on k vertices that contains the largest number of edges. Expand
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Smoothed analysis of tensor decompositions
TLDR
We show that tensor products of perturbed vectors are linearly independent in a robust sense in the framework of smoothed analysis. Expand
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Approximation algorithms for semi-random partitioning problems
In this paper, we propose and study a new semi-random model for graph partitioning problems. We believe that it captures many properties of real-world instances. The model is more flexible than theExpand
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On Learning Mixtures of Well-Separated Gaussians
TLDR
We consider the problem of efficiently learning mixtures of a large number of spherical Gaussians, when the components of the mixture are well separated. Expand
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Learning Mixtures of Ranking Models
TLDR
We present the first polynomial time algorithm which provably learns the parameters of a mixture of two Mallows models. Expand
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Approximating matrix p-norms
TLDR
We consider the problem of computing the ↦ ↦ <i>p</i> norm of a matrix with non-negative entries, which is defined for < i>p, q</I> ≥ 1, as a non-convex optimization problem, and present an efficient algorithm for computing it. Expand
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Bilu-Linial Stable Instances of Max Cut and Minimum Multiway Cut
TLDR
We investigate the notion of stability proposed by Bilu and Linial. Expand
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Clustering Stable Instances of Euclidean k-means
TLDR
We design efficient algorithms that provably recover the optimal clustering for instances that are additive perturbation stable for the Euclidean k-means clustering problem. Expand
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Beating the random assignment on constraint satisfaction problems of bounded degree
TLDR
We show that for any odd k and any instance I of the max-kXOR constraint satisfaction problem, there is an efficient algorithm that finds an assignment satisfying at least a 1/2 + Omega(1/sqrt(D)) fraction of I's constraints, where D is a bound on the number of constraints that each variable occurs in. Expand
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On Robustness to Adversarial Examples and Polynomial Optimization
TLDR
We study the design of computationally efficient algorithms with provable guarantees, that are robust to adversarial (test time) perturbations. Expand
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