On the positive side, researchers have recently developed tools for measuring how gerrymandered a redistricting map is by comparing it to a large set of randomly-generated district maps.
In the most general form, the platform consists of three entities: two sides to be matched and a platform operator that decides the matching.
We derive fundamental lower bounds on the approximation of the utilitarian and egalitarian objectives and introduce algorithms with provable guarantees for them.
Clustering is a fundamental problem in unsupervised machine learning, and fair variants of it have recently received significant attention due to its societal implications.
In fair clustering problems, vertices are endowed with a color (e. g., membership in a group), and the features of a valid clustering might also include the representation of colors in that clustering.
Overall, by combining the sensitivity and utility characterization, we obtain an end-to-end differentially private spectral algorithm for LDA and identify the corresponding configuration that outperforms others in any specific regime.