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We study the maximum coverage problem for geometric set systems: given a set of points, a set of geometric objects, and a number $k$, select $k$ objects maximizing the number of points inside their union. - We present a polynomial-time approximation algorithm with approximation factor strictly better than $1-1/e$ for a...
We study the question of answering linear queries with differential privacy using few (expected) random bits. We provide a randomness-efficient analog of the $\| \cdot \|_K$-norm mechanism of Hardt and Talwar [HT10]. For the $\ell_\infty$-error, our algorithm can answer $d$ linear queries with $O(d / \varepsilon)$ erro...
We study combinatorial optimization problems under the constraint of $\epsilon$-differential privacy ($\epsilon$-DP). Given the strong lower bounds for explicitly outputting solutions, we work within the implicit representation framework of Gupta et al. (SODA 2010), where a private polynomial-time randomized"encoder"ge...
Differential privacy protects individual voting records by injecting randomness into the published outcome, but this noise can lead to erroneous results when an election is close. We study how precise central differential privacy and local differential privacy can be for common voting rules, including Plurality, Condor...
A generic reduction is given that transforms the (sensitive) input stream into a private stream, which is a semi-coreset of the input stream, which implies that any (non-private) online clustering algorithm, run as a post-processing step, can achieve good utility for the original clustering objective.
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