Sublinear Space Graph Algorithms in the Continual Release Model

2026-04-16T17:38:02+00:00

The graph continual release model of differential privacy seeks to produce differentially private solutions to graph problems under a stream of edge updates where new private solutions are released after each update. Previously known edge differentially private algorithms for most graph problems including densest subgraph and matchings in the continual release setting only output real-valued estimates (not vertex subset solutions) and do not use sublinear space. In this paper, we leverage sparsification to address the above shortcomings for edge-insertion streams. Our edge differentially private algorithms use sublinear space with respect to the number of edges in the graph. In addition, for the densest subgraph problem, we output edge differentially private vertex subset solutions; no previous graph algorithms in the continual release model output such subsets.

We make novel use of sparsification techniques from the non-private streaming and static graph algorithms literature to achieve new results in the sublinear space continual release setting. This includes algorithms for densest subgraph, maximum matching, and the first continual release k-core decomposition algorithm. To complement our insertion-only algorithms, we conclude with polynomial additive error lower bounds for edge-privacy in the fully dynamic setting, where only logarithmic lower bounds were previously known.

Prior Distributions for Gaussian Models Under Differential Privacy with Bounds on Data Values

2026-03-16T16:56:29+00:00

The Gaussian distribution is often used to model univariate, numerical data, even in contexts where individuals' data values are bounded, e.g., test scores and biological measurements. We consider Bayesian inference for the parameters of Gaussian models when (i) analysts seek a post-processing algorithm that takes noisy sufficient statistics as inputs and produces a posterior distribution of the parameters as output, and (ii) the privacy mechanism enforces bounds on individual data values as a condition for satisfying pure differential privacy. Our primary contributions focus on the specification of prior distributions for model parameters. Specifically, we illustrate that failing to account for the bounds on data values when using informative prior distributions can result in posterior inferences with undesirable properties. Further, we show theoretically that the usual default priors used in the nonprivate setting do not lead to proper posterior distributions, and we suggest a default prior distribution that does. We also show empirically that one can improve the performance of inferential procedures by incorporating the boundedness assumptions into the specification of prior distributions. We present methods for inferring about the mean and variance of a univariate Gaussian model and the coefficients and variance of a linear regression. As we discuss, the general strategies used for the Gaussian models can be adapted for other models when enforcing bounds on the data values to ensure differential privacy.

Journal of Privacy and Confidentiality

Sublinear Space Graph Algorithms in the Continual Release Model

Prior Distributions for Gaussian Models Under Differential Privacy with Bounds on Data Values