Publishing Below-Threshold Triangle Counts under Local Weight Differential Privacy

2026-01-05

arXiv.org

AI Summary

This study addresses the problem of accurately counting triangles with total edge weight below a given threshold in edge-weight-sensitive public graphs while satisfying Local Weight Differential Privacy (LWDP). To this end, the authors propose a two-round distributed mechanism: in the first round, each node locally perturbs and publishes its incident edge weights; in the second round, nodes use the perturbed data to locally estimate the target triangle count, employing both biased and unbiased estimators. The main contributions include the first application of LWDP to weighted triangle counting, the introduction of a precomputation step to reduce covariance and estimation error, and an efficient smooth sensitivity algorithm that significantly improves computational efficiency. Experimental results demonstrate the superiority of the proposed approach in terms of both accuracy and runtime performance.

Technology Category

• Machine Learning: Privacy
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Local Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

We propose an algorithm for counting below-threshold triangles in weighted graphs under local weight differential privacy. While prior work focused on unweighted graphs, many real-world networks naturally include edge weights. We study the setting where the graph topology is public known and the privacy of the influence of an individual on the edge weights is protected. This captures realistic scenarios such as road networks and telecommunication networks. Our approach consists of two rounds of communication. In the first round, each node publishes their incident weight information under local weight differential privacy while in the second round, the nodes locally count below-threshold triangles, for which we introduce a biased and unbiased variant. We further propose two different improvements. We present a pre-computation step that reduces the covariance and thereby lowers the expected error. Secondly, we develop an algorithm for computing the smooth-sensitivity, which significantly reduces the running time compared to a straightforward approach. Finally, we provide experimental results that demonstrate the differences between the biased and unbiased variants and the effectiveness of the proposed improvements.

Problem

• local weight differential privacy
• below-threshold triangle counting
• weighted graphs
• privacy-preserving graph analysis
• edge weights

Innovation

• local weight differential privacy
• weighted graph triangle counting
• below-threshold triangles
• smooth sensitivity
• pre-computation covariance reduction