Existence of a universally stable time-aware projection for node privacy

Determine whether there exists a time-aware projection algorithm for graph streams that maps any input stream to a D-bounded stream and has low node-to-node stability uniformly over all inputs; that is, for every pair of node-neighboring graph streams S and S', the node distance between the projected streams is bounded by a small function independent of the stream length and without requiring any (D, l)-bounded safety condition. Establishing such a projection would allow a D-restricted node-differentially private base algorithm to yield an unconditionally node-private algorithm by running it on the projected stream.

Background

The paper develops time-aware projection algorithms that enforce a degree bound D on streaming graphs and analyzes their stability. These projections enable transforming D-restricted private algorithms into unconditionally private ones when inputs satisfy a privately testable (D, l)-bounded safety condition.

A central bottleneck is achieving node privacy without such a safety condition. If a projection had uniformly low node-to-node stability on all inputs, simply running any D-restricted node-private algorithm on the projected stream would suffice for unconditional node privacy. The authors show an analogous transformation exists for edge privacy via a projection with constant edge sensitivity, but whether an equally strong projection exists for node privacy remains unknown.