We suggest the use of hash functions to cut down the communication costs when counting subgraphs under edge local differential privacy. While various algorithms exist for computing graph statistics, including the count of subgraphs, under the edge local differential privacy, many suffer with high communication costs, making them less efficient for large graphs. Though data compression is a typical approach in differential privacy, its application in local differential privacy requires a form of compression that every node can reproduce. In our study, we introduce linear congruence hashing. With a sampling rate of $s$, our method can cut communication costs by a factor of $s^2$, albeit at the cost of increasing variance in the published graph statistic by a factor of $s$. The experimental results indicate that, when matched for communication costs, our method achieves a reduction in the $\ell_2$-error for triangle counts by up to 1000 times compared to the performance of leading algorithms.

翻译：我们提出利用哈希函数来降低边局部差分隐私下子图计数过程中的通信成本。尽管现有多种算法可在边局部差分隐私下计算图统计量（包括子图计数），但许多算法因通信成本高昂而难以高效应用于大规模图。虽然数据压缩是差分隐私中的典型方法，但其在局部差分隐私中的应用需要一种每个节点都能复现的压缩形式。在本研究中，我们引入线性同余哈希。在采样率为$s$的条件下，我们的方法可将通信成本降低$s^2$倍，但代价是公开图统计量的方差增大$s$倍。实验结果表明，在通信成本匹配的情况下，与主流算法相比，本方法在三角形计数的$\ell_2$误差上最高可降低1000倍。