Tight error bounds for differentially private APSD

Determine tight asymptotic additive error bounds for the (ε,δ)-differentially private all-pairs shortest distances problem on n-node undirected graphs by closing the gap between the current Ω(n^{1/4}) lower bound (up to polylogarithmic factors) and the best known O(n^{1/2}) upper bound.

Background

Using the new hereditary discrepancy lower bound for unique shortest paths, the paper improves the lower bound on additive error for DP-APSD to order n^{1/4} (up to polylogarithmic factors).

Despite this, the best algorithmic upper bound for DP-APSD remains O(n^{1/2}), leaving a polynomial gap between lower and upper bounds that needs to be resolved.