Communication-Efficient Triangle Counting under Local Differential Privacy

TL;DR

This paper introduces communication-efficient algorithms for triangle counting under local differential privacy, significantly reducing communication costs while maintaining low estimation error in network analysis.

Contribution

It proposes novel two-round algorithms with edge sampling and a double clipping technique to minimize communication and estimation error under LDP.

Findings

Reduces communication time from hours to seconds at 20 Mbps.

Maintains small estimation error with fewer communication resources.

Demonstrates effectiveness through comprehensive evaluation.

Abstract

Triangle counting in networks under LDP (Local Differential Privacy) is a fundamental task for analyzing connection patterns or calculating a clustering coefficient while strongly protecting sensitive friendships from a central server. In particular, a recent study proposes an algorithm for this task that uses two rounds of interaction between users and the server to significantly reduce estimation error. However, this algorithm suffers from a prohibitively high communication cost due to a large noisy graph each user needs to download. In this work, we propose triangle counting algorithms under LDP with a small estimation error and communication cost. We first propose two-rounds algorithms consisting of edge sampling and carefully selecting edges each user downloads so that the estimation error is small. Then we propose a double clipping technique, which clips the number of edges and then the number of noisy triangles, to significantly reduce the sensitivity of each user's query. Through comprehensive evaluation, we show that our algorithms dramatically reduce the communication cost of the existing algorithm, e.g., from 6 hours to 8 seconds or less at a 20 Mbps download rate, while keeping a small estimation error.