This is the first formal analysis of the effect of instance-based noise in the context of data privacy, and shows how to do this efficiently for several different functions, including the median and the cost of the minimum spanning tree.Expand

This work investigates learning algorithms that satisfy differential privacy, a notion that provides strong confidentiality guarantees in the contexts where aggregate information is released about a database containing sensitive information about individuals.Expand

A generic, efficient reduction is derived that allows us to apply any differentially private algorithm for bounded-degree graphs to an arbitrary graph, based on analyzing the smooth sensitivity of the 'naive' truncation that simply discards nodes of high degree.Expand

This work extends the approach of Nissim et al. to a new class of statistics, namely k-star queries, and gives hardness results indicating that the approach used for triangles cannot easily be extended to k-triangles.Expand

It is shown that in its most general setting, testing that Boolean functions are close to monotone is equivalent, with respect to the number of required queries, to several other testing problems in logic and graph theory.Expand

It is proved that there are 3CNF properties that require a linear number of queries, even for adaptive tests, which contrasts with 2C NF properties that are testable with O(√n) queries.Expand

The problem of approximating the support size of a distribution from a small number of samples, when each element in the distribution appears with probability at least 1/n is considered, and a nearly linear in n lower bound on the query complexity is proved.Expand

An O(nlogn)-approximation algorithm for the problem of finding the sparsest spanner of a given directed graph G on n vertices is presented and the approximation ratio almost matches Dinitz and [email protected]?s lower bound for the integrality gap of a natural linear programming relaxation.Expand

Improved algorithms for testing monotonicity of functions are presented, given the ability to query an unknown function f: Σ n ↦ Ξ, and the test always accepts a monotone f, and rejects f with high probability if it is e-far from being monotones.Expand

The common task implicitly tackled in these diverse applications as the problem of constructing sparse TC-spanners is abstracted asThe study of approximability of the size of the sparsest of a given directed graph is initiated.Expand