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 large 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-round 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 20 Mbps download rate, while keeping a small estimation error.

翻译：在LDP(本地差异隐私)下的网络中计三角是分析连接模式或计算组合系数,同时大力保护敏感友谊不受中央服务器影响的一项基本任务。 特别是,最近的一项研究为这项任务提出了一个算法,使用用户和服务器之间的两轮互动来大大减少估计误差。 但是,由于每个用户都需要下载一个大吵的图形,这种算法的通信费用极高,令人望而却步。 在这项工作中,我们提议在LDP下提出三角计算算法,其估计误差和通信费用较小。我们首先提出由边缘抽样组成的双轮算法,并仔细选择每个用户下载的边缘,以便估计误差很小。 然后我们提出一种双轨算法,用于剪切边缘数,然后剪切扰动三角形的数目,以大幅降低每个用户查询的敏感度。我们通过全面评价,表明我们的算法大大降低了现有算法的通信费用,例如,从6小时到8秒或不到20Mbps下载率,同时保持一个小的估算误差。