# Open Problem: Private All-Pairs Distances

**Background:** Suppose we are interested in computing the distance between two vertices in a graph. Under edge or node differential privacy, this problem is not promising because the removal of a single edge can make distances change from 1 to \(n − 1\) or can even disconnect the graph. However, a different setting that makes sense to consider is that of a weighted graph \((G, w)\) whose topology \(G = (V, E)\) is publicly known but edge weight function \(w : E \to \mathbb{R}^+\) must be kept private. (For instance, consider transit times on a road network. The topology of the road network may be publicly available as a map, but the edge weights corresponding to transit times may be based on private GPS locations of individual cars.)