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.

翻译：本文针对低树宽图类，提出一种多项式时间算法，用于解决差分隐私下的全对最短距离问题。该结果将Sealfon（2016）针对树结构的研究推广至更广泛的图族。此外，若限定于低树宽图类，本文算法的加性误差显著小于Chen等人（2023）提出的同类问题现有最优算法。