Sparse discrete-Laplace and Gaussian local DP mechanisms admit exact privacy characterizations, with support cardinality as the key parameter that sets a minimum size for nontrivial approximate privacy and yields an optimal smallest-support design rule.
Mechanism design via differential privacy
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Sparse Discrete Laplace and Gaussian Mechanisms under Local Differential Privacy
Sparse discrete-Laplace and Gaussian local DP mechanisms admit exact privacy characterizations, with support cardinality as the key parameter that sets a minimum size for nontrivial approximate privacy and yields an optimal smallest-support design rule.