Communication Cost Reduction for Subgraph Counting under Local Differential Privacy via Hash Functions

TL;DR

This paper introduces a hashing-based method to significantly reduce communication costs in subgraph counting under local differential privacy, achieving up to 1000 times lower error at comparable costs.

Contribution

The study proposes linear congruence hashing to lower communication costs in local differential privacy for subgraph counting, balancing efficiency and variance.

Findings

Communication costs reduced by a factor of s^2

Up to 1000 times lower $ ext{l}_2$-error in triangle counts

Method matches existing algorithms in communication efficiency

Abstract

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.