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

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 the… Expand

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

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

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

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