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An algorithm is presented for exactly solving (in fact, counting) the number of maximum weight satisfying assignments of a 2-Cnf formula. The worst case running time of O(1.246 n) for formulas with n variables improves on the previous bound of O(1.256 n) by Dahllöf, Jonsson, and Wahlström. The algorithm uses only polynomial space. As a consequence we get an… (More)

We describe novel subgradient methods for a broad class of matrix optimization problems involving nuclear norm regularization. Unlike existing approaches, our method executes very cheap iterations by combining low-rank stochastic subgradients with efficient incremental SVD updates, made possible by highly optimized and parallelizable dense linear algebra… (More)

Learning problems form an important category of computational tasks that generalizes many of the computations researchers apply to large real-life data sets. We ask: what concept classes can be learned privately, namely, by an algorithm whose output does not depend too heavily on any one input or specific training example? More precisely, we investigate… (More)

We develop algorithms for the private analysis of network data that provide accurate analysis of realistic networks while satisfying stronger privacy guarantees than those of previous work. We present several techniques for designing node differentially private algorithms, that is, algorithms whose output distribution does not change significantly when a… (More)

Privacy is an increasingly important aspect of data publishing. Reasoning about privacy, however, is fraught with pitfalls. One of the most significant is the auxiliary information (also called external knowledge, background knowledge, or side information) that an adversary gleans from other channels such as the web, public records, or domain knowledge.… (More)

Streaming user-generated content in the form of blogs, microblogs, forums, and multimedia sharing sites, provides a rich source of data from which invaluable information and insights maybe gleaned. Given the vast volume of such social media data being continually generated, one of the challenges is to automatically tease apart the emerging topics of… (More)

Learning is a task that generalizes many of the analyses that are applied to collections of data, in particular, to collections of sensitive individual information. Hence, it is natural to ask what can be learned while preserving individual privacy. Kasiviswanathan et al. (in SIAM J. Comput., 40(3):793–826, 2011) initiated such a discussion. They formalized… (More)

Motivated by the widespread proliferation of wireless networks employing directional antennas, we study some capacitated covering problems arising in these networks. Geometrically, the area covered by a directional antenna with parameters α,ρ,<i>r</i> is a set of points with polar coordinates (<i>r</i>,θ) such that <i>r</i> ≤ <i>r</i>… (More)

EEcient algorithms are presented for constructing spanners in geometric intersection graphs. For a unit ball graph in R k , a (1 +)-spanner with O(nn-k+1) edges is obtained using eecient partitioning of the space into hypercubes and solving bichromatic closest pair problems. The spanner construction has almost equivalent complexity to the construction of… (More)

A disk graph is an intersection graph of a set of disks with arbitrary radii in the plane. Given a real number t > 1, we say that a subgraph G ′ of a graph G is a t-spanner for G, if for every pair of vertices u, v in G, there exists a path in G ′ of length at most t times the distance between u and v in G. In this paper, we consider the problem of… (More)