@article{Gu_Zhou_Günlü_D’Oliveira_Sadeghi_Médard_Schaefer_2024, title={Generalized Rainbow Differential Privacy}, volume={14}, url={https://journalprivacyconfidentiality.org/index.php/jpc/article/view/896}, DOI={10.29012/jpc.896}, abstractNote={<p>We study a new framework for designing differentially private (DP) mechanisms via randomized graph colorings, called rainbow differential privacy. In this framework, datasets are nodes in a graph, and two neighboring datasets are connected by an edge. Each dataset in the graph has a preferential ordering for the possible outputs of the mechanism, and these orderings are called rainbows. Different rainbows partition the graph of connected datasets into different regions. We show that if a DP mechanism at the boundary of such regions is fixed and it behaves identically for all same-rainbow boundary datasets, then a unique optimal $(\epsilon,\delta)$-DP mechanism exists (as long as the boundary condition is valid) and can be expressed in closed-form. Our proof technique is based on an interesting relationship between dominance ordering and DP, which applies to any finite number of colors and for $(\epsilon,\delta)$-DP, improving upon previous results that only apply to at most three colors and for $\epsilon$-DP. We justify the homogeneous boundary condition assumption by giving an example with non-homogeneous boundary condition, for which there exists no optimal DP mechanism.</p>}, number={2}, journal={Journal of Privacy and Confidentiality}, author={Gu, Yuzhou and Zhou, Ziqi and Günlü, Onur and D’Oliveira, Rafael G. L. and Sadeghi, Parastoo and Médard, Muriel and Schaefer, Rafael F.}, year={2024}, month={Jun.} }