All-Pairs Shortest Path Distances with Differential Privacy: Improved Algorithms for Bounded and Unbounded Weights. (arXiv:2204.02335v1 [cs.DS])

We revisit the problem of privately releasing the all-pairs shortest path
distances of a weighted undirected graph up to low additive error, which was
first studied by Sealfon [Sea16]. In this paper, we improve significantly on
Sealfon's results, both for arbitrary weighted graphs and for bounded-weight
graphs on $n$ nodes. Specifically, we provide an approximate-DP algorithm that
outputs all-pairs shortest path distances up to maximum additive error
$\tilde{O}(\sqrt{n})$, and a pure-DP algorithm that outputs all pairs shortest
path distances up …

algorithms differential privacy ds path privacy