Truss Decomposition Under Edge Local Differential Privacy

k-truss is a widely studied cohesive sub graph model that has gained significant attention over the past decades. Truss decomposition, a fundamental task in graph analysis, aims to compute the largest k for which an edge belongs to a k-truss. However, directly performing truss decomposition on sensitive graphs risks exposing the private information of user connections in real-world applications. Edge local differential privacy (edge LDP) is extensively used to protect the privacy of edges in graph analysis. This paper, for the first time, addresses the problem of truss decomposition under edge LDP. A naive approach allows each vertex to perturb its neighbor list locally and generate a noisy graph for truss decomposition. However, it often produces excessive truss number estimations, since the noisy graph is generally much denser and fails to preserve the input graph structure. To obtain more accurate estimates, we propose the Local algorithm that leverages the local information during the truss decomposition process. Furthermore, to avoid adding substantial noise to truss numbers to satisfy edge LDP, we introduce the Global algorithm that optimizes the noise scale of support numbers, enhancing the accuracy of truss decom-position results. We further propose the Global * algorithm that eliminates the need for vertices to download noisy edges by utilizing noisy degrees to adjust support numbers during truss decomposition, achieving high accuracy with significantly lower communication costs. Extensive experiments on 9 real-world datasets demonstrate the effectiveness and efficiency of our proposed algorithms.