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.

翻译：在局部差分隐私（LDP）框架下对网络进行三角形计数，是分析连接模式或计算聚类系数的基本任务，同时能强有力地保护敏感友谊关系免受中心服务器的窥探。特别地，近期一项研究提出了一种利用用户与服务器间两轮交互来显著降低估计误差的算法。然而，该算法因每个用户需下载包含大量噪声的图结构，导致通信成本过高而难以实用。本文提出了一种兼具低估计误差与低通信成本的LDP三角形计数算法。首先，我们设计了两轮算法，通过边采样策略并精心选择每个用户需下载的边集，实现较小的估计误差。随后提出双重截断技术，分别对边数量与噪声三角形数量进行截断，从而显著降低每个用户查询的敏感度。综合评估表明，与现有算法相比，本文算法在保持较小估计误差的同时，将通信成本从6小时（20 Mbps下载速率）大幅缩减至8秒甚至更短。