CSDM Seminars

We prove a complexity dichotomy theorem for all non-negatively weighted counting Constraint Satisfaction Problems (#CSP). This caps a long series of important results on counting problems including unweighted and weighted graph homomorphisms and the...

Consider an optimization problem with n binary variables and d+1 linear objective functions. Each valid solution x in {0,1}^n gives rise to an objective vector in R^{d+1}, and one often wants to enumerate the Pareto optima among these. In the worst...

We define a polynomial threshold function to be a function of the form f(x) = sgn(p(x)) for p a polynomial. We discuss some recent techniques for dealing with polynomial threshold functions, particular when evaluated on random Gaussians. We show how...

It is well-known that any Boolean function f:{-1,+1}^n \to {-1,+1} can be written uniquely as a polynomial f(x) = \sum_{S subset [n]} f_s \prod_{i in S} x_i. The collection of coefficients (f_S's) this expression are referred to (with good reason)...

Non-relativization of complexity issues can be interpreted as giving evidence that these issues cannot be resolved by “black-box” techniques. We show that the assumption $DistNP \subseteq AvgP$ does not imply that $NP\subseteq BPP$ by relativizing...

We show a (3/2-\epsilon)-approximation algorithm for the graphical traveling salesman problem where the goal is to find a shortest tour in an unweighted graph G. This is a special case of the metric traveling salesman problem when the underlying...

Property testing considers the following general question: how many queries to some combinatorial object (e.g., a boolean function or a graph) do we need to determine whether the object has some property P or whether it is "far" from having the...

We prove completeness results for certain class of functions which have implications for automatic proving of universally-composable security theorems for ideal and real functionalities composed of if-then-else programs with (uniform) random number...

We study the local testabilty of sparse linear codes. This problem is intimately connected to the problem of tolerant linearity testing of Boolean functions under nonuniform distributions. We give linearity tests for several natural and interesting...