Differentially Private All-Pairs Shortest Distances for Low Tree-Width Graphs

TL;DR

This paper introduces a polynomial-time algorithm for computing all-pairs shortest distances privately in low tree-width graphs, extending previous work on trees and improving error bounds.

Contribution

It generalizes differentially private shortest path algorithms from trees to low tree-width graphs with improved accuracy.

Findings

Algorithm runs in polynomial time.

Achieves smaller additive error than previous methods.

Extends privacy-preserving shortest path computation to broader graph classes.

Abstract

In this paper, we present a polynomial time algorithm for the problem of differentially private all pair shortest distances over the class of low tree-width graphs. Our result generalizes the result of Sealfon 2016 for the case of trees to a much larger family of graphs. Furthermore, if we restrict to the class of low tree-width graphs, the additive error of our algorithm is significantly smaller than that of the best known algorithm for this problem, proposed by Chen et. al. 2023.