Large-scale social networks can be modeled as decentralized graphs, where each node holds a part of the overall network. Local differential privacy (LDP) has been widely adopted in decentralized graph analysis to ensure privacy for individual nodes. However, existing LDP-based methods often fail to accommodate personalized privacy requirements due to their uniform encoding and equal perturbation mechanisms. To address this issue, we propose PEGS, a novel privacy-preserving decentralized graph synthesis approach that significantly improves utility while respecting user-specific privacy preferences. Specifically, we introduce interactive local differential privacy (iLDP), a new edge-level definition of LDP that relaxes the constraints of node-independent perturbation, thereby enabling the fulfillment of individual privacy needs. Furthermore, we develop a decentralized graph perturbation framework offering three levels of privacy settings. To optimize the balance between information preservation and privacy, we design encoding and perturbation mechanisms leveraging information entropy tailored to different privacy levels. Extensive experimental evaluations and rigorous theoretical analysis demonstrate that our method produces high-quality synthetic graphs while adhering to iLDP guarantees.

The goal of privacy-preserving social graph publishing is to protect individual privacy while preserving data utility. Community structure, which is an important global pattern of nodes, is a crucial data utility as it serves as fundamental operations for many graph analysis tasks. Yet, most existing methods with differential privacy (DP) commonly fall in edge-DP to sacrifice security in exchange for utility. Moreover, they reconstruct graphs from the local feature-extraction of nodes, resulting in poor community preservation. Motivated by this, we propose PrivCom, a strict node-DP graph publishing algorithm to maximize the utility on the community structure while maintaining a higher level of privacy. Specifically, to reduce the huge sensitivity, we devise a Katz index-based private graph feature extraction method, which can capture global graph structure features while greatly reducing the global sensitivity via a sensitivity regulation strategy. Yet, with a fixed sensitivity, the feature captured by Katz index, which is presented in matrix form, requires privacy budget splits. As a result, plenty of noise is injected, thereby mitigating global structural utility. To this end, we design a private Oja algorithm approximating eigen-decomposition, which yields the noisy Katz matrix via privately estimating eigenvectors and eigenvalues from extracted low-dimensional vectors. Experimental results confirm our theoretical findings and the efficacy of PrivCom.

Performance and scalability are two issues that are becoming increasingly pressing as RDF data model is applied to real-world applications. Because neither vertical nor flat structures of RDF storage can handle frequent schema updates and meanwhile avoid possible long-chain joins, there is no clear winner between these two typical structures. In this paper, we propose an alternative storage schema called open user schema. The open user schema consists of flat tables automatically extracted from RDF query streams. A query is divided into two parts and conquered,respectively, on the flat tables in the open user schema and on the vertical table stored in a backend storage. At the core of this divide and conquer architecture with open user schema, an efficient isomorphism decision algorithm is given to guide a query to related flat tables in the open user schema. Our proposal in essence departs from existing methods in that it can accommodate schema updates without possible long-chain joins. We implement our approach and provide empirical evaluations to demonstrate both efficiency and effectiveness of our approach in evaluating complex RDF queries.