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Differentially Private Matching in General Graphs

Design and analyze differentially private algorithms that compute the actual matching (the edge set), not merely its size, for maximum matching and b-matching in general graphs. Reason about why any DP explicit matching must be permitted to output non-edges, derive lower bounds showing a utility-versus-degree trade-off, and construct implicit-solution mechanisms achieving tight bicriteria bounds under edge-privacy, node-privacy, local edge-DP, and continual release.