Graph pattern counting serves as a cornerstone of network analysis with extensive real-world applications. Its integration with local differential privacy (LDP) has gained growing attention for protecting sensitive graph information in decentralized settings. However, existing LDP frameworks are largely ad hoc, offering solutions only for specific patterns such as triangles and stars. A general mechanism for counting arbitrary graph patterns, even for the subclass of acyclic patterns, has remained an open problem. To fill this gap, we present the first general solution for counting arbitrary acyclic patterns under LDP. We identify and tackle two fundamental challenges: generalizing pattern construction from distributed data and eliminating node duplication during the construction. To address the first challenge, we propose an LDP-tailored recursive subpattern counting framework that incrementally builds patterns across multiple communication rounds. For the second challenge, we apply a random marking technique that restricts each node to a unique position in the pattern during computation. Our mechanism achieves strong utility guarantees: for any acyclic graph pattern with $k$ edges, we achieve an additive error of $\tilde{O}(\sqrt{N}d(G)^k)$, where $N$ is the number of nodes and $d(G)$ is the maximum degree of the input graph $G$. Experiments on real-world graph datasets across multiple types of acyclic patterns demonstrate that our mechanisms achieve up to $46$-$2600\times$ improvement in utility and $300$-$650\times$ reduction in communication cost compared to the baseline methods.

翻译：图模式计数作为网络分析的基石，在现实世界中有广泛的应用。它与局部差分隐私（LDP）的结合因能在去中心化场景中保护敏感图信息而日益受到关注。然而，现有的LDP框架大多具有特殊性，仅针对特定模式（如三角形和星形）提供解决方案。即使对于无环模式子类，对任意图模式进行计数的通用机制仍然是一个未解决的问题。为填补这一空白，我们提出了首个在LDP下对任意无环模式进行计数的通用解决方案。我们识别并解决了两个基本挑战：从分布式数据中泛化模式构建，以及在此构建过程中消除节点重复。针对第一个挑战，我们提出了一种面向LDP的递归子模式计数框架，该框架通过多轮通信逐步构建模式。针对第二个挑战，我们应用了一种随机标记技术，在计算过程中将每个节点限制到模式中的唯一位置。我们的机制实现了强大的效用保证：对于任意包含$k$条边的无环图模式，我们实现了$\tilde{O}(\sqrt{N}d(G)^k)$的加性误差，其中$N$是节点数，$d(G)$是输入图$G$的最大度数。在多种无环模式类型的真实图数据集上的实验表明，与基线方法相比，我们的机制在效用上实现了高达$46$-$2600$倍的提升，在通信开销上减少了$300$-$650$倍。