Subgraph counting is a fundamental problem in graph analysis. Motivated by practical scenarios where graph analytics are performed on subgraphs induced by selected vertices -- rather than on the entire graph -- and by growing privacy concerns, we initiate the study of differentially private range subgraph counting (DPRSC). The goal is to privately count occurrences of a fixed pattern graph within induced subgraphs defined by multi-dimensional attribute ranges. Unlike classical point counting, subgraph counting is inherently nonlinear and exhibits high sensitivity: a single edge modification can affect many subgraph occurrences. We present the first efficient algorithms for DPRSC with small additive error. Our approach introduces a subgraph projection that reduces DPRSC to weighted orthogonal range counting, enabling the use of range trees and local sensitivity estimation to achieve accurate private query answering. We complement our algorithms with matching lower bounds, obtained by reducing reconstruction attacks to DPRSC and leveraging discrepancy theory. In particular, we show that any differentially private algorithm for DPRSC must incur additive error exponential in the dimension. Empirical evaluations demonstrate that our algorithms significantly outperform baseline methods in accuracy and runtime while maintaining strong privacy guarantees.

翻译：子图计数是图分析中的一个基本问题。受实际场景的驱动（图分析往往针对选定顶点所诱导的子图而非整个图进行）以及日益增长的隐私关切，我们首次开展了差分隐私范围子图计数（DPRSC）的研究。其目标是在由多维属性范围定义的诱导子图中，对固定模式图的出现次数进行隐私保护下的计数。与经典的点计数不同，子图计数本质上是非线性的且具有高敏感性：单条边的修改就可能影响大量子图出现次数。我们提出了首个具有小加法误差的高效DPRSC算法。我们的方法引入了一种子图投影，将DPRSC归约为带权正交范围计数，从而能够利用范围树和局部敏感性估计来实现精确的隐私查询回答。我们通过将重构攻击归约为DPRSC并利用差异理论，给出了与算法相匹配的下界。特别地，我们证明了任何针对DPRSC的差分隐私算法都必须承受随维度呈指数增长的加法误差。实验评估表明，我们的算法在精度和运行时间上显著优于基线方法，同时保持了强大的隐私保障。