A result of Johnson and Lindenstrauss [13] shows that a set of n points in high dimensional Euclidean space can be mapped into an O(log n/ )-dimensional Euclidean space such that the distance betweenâ€¦ (More)

The Johnson-Lindenstrauss lemma shows that a set of n points in high dimensional Euclidean space can be mapped down into an O(log n== 2) dimensional Euclidean space such that the distance between anyâ€¦ (More)

Consider a setting in which a group of nodes, situated in a large underlying network, wishes to reserve bandwidth on which to support communication. Virtual private networks (VPNs) are services thatâ€¦ (More)

The doubling constant of a metric space(X; d) is the smallest value such that every ball inX can be covered by balls of half the radius. Thedoubling dimensionof X is then defined as dim(X) = log2 . Aâ€¦ (More)

Approximation algorithms for clustering points in metric spaces is a flourishing area of research, with much research effort spent on getting a better understanding of the approximation guaranteesâ€¦ (More)

We give simple and easy-to-analyze randomized approximation algorithms for several well-studied NP-hard network design problems. Our algorithms improve over the previously best known approximationâ€¦ (More)

Several combinatorial optimization problems choose elements to minimize the total cost of constructing a feasible solution that satisfies requirements of clients. In the Steiner Tree problem, forâ€¦ (More)

In this paper we study the problem of approximately releasing the cut function of a graph while preserving differential privacy, and give new algorithms (and new analyses of existing algorithms) inâ€¦ (More)

We give a simple algorithm for the Minimum Directed Multicut problem, and show that it gives an <i>O</i>(âˆš<i>n</i>)-approximation. This improves on the previous approximation guarantee ofâ€¦ (More)