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

TMLR Paper4676 Authors

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. Leveraging amplification by sub-sampling, with a sampling size 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 by up to 1000 times for triangle counts and by up to $10^3$ times for 4-cycles counts compared to the performance of leading algorithms.

Submission Length: Long submission (more than 12 pages of main content)

Assigned Action Editor: ~Kamalika_Chaudhuri1

Submission Number: 4676