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We generalize a previous framework for designing utility-optimaldifferentially private (DP) mechanisms via graphs, where datasets are verticesin the graph and edges represent dataset neighborhood. The boundary setcontains datasets where an individual's response changes the binary-valuedquery compared to its neighbors. Previous work was limited to the homogeneouscase where the privacy parameter $\varepsilon$ across all datasets was the sameand the mechanism at boundary datasets was identical. In our work, themechanism can take different distributions at the boundary and the privacyparameter $\varepsilon$ is a function of neighboring datasets, which recoversan earlier definition of personalized DP as special case. The problem is how toextend the mechanism, which is only defined at the boundary set, to otherdatasets in the graph in a computationally efficient and utility optimalmanner. Using the concept of strongest induced DP condition we solve thisproblem efficiently in polynomial time (in the size of the graph).

Heterogeneous Differential Privacy via Graphs