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A polynomial-time approximation algorithm with approximation factor strictly better than $1-1/e$ for any set system with linear 2-shallow cell complexity and any set system that can be decomposed into a constant number of such set systems is presented.
The algorithm can answer linear queries with differential privacy using few (expected) random bits using $O(d / \varepsilon)$ error using $O(\log d)$ random bits, improving upon algorithms of Canonne et al. and Ghentiyala.
This work generalizes the implicit representation framework of Gupta et al. (SODA 2010) by allowing the encoder to run in fixed-parameter tractable time, and provides representation-dependent lower bounds that hold even for larger $\epsilon$.
This work studies how precise central differential privacy and local differential privacy can be for common voting rules, including Plurality, Condorcet, Maximin, Plurality with Runoff, and Single Transferable Vote, and proves upper bounds on the required margin for these algorithms.
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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