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原文摘要

Range counting over vertex statistics supports contact analysis, community profiling, and reputation screening. However, releasing exact range counts can disclose sensitive edges to an adversary with background knowledge. We study this problem under edge local differential privacy (edge LDP), where each vertex randomizes its report before sending it to an untrusted curator. We develop a layered framework that connects statistic estimation, direct range estimation, and adaptive estimator selection. Statistic-estimation methods provide complementary scalar estimators with explicit loss analyses, while indicator-estimation methods privatize range indicators directly. We next propose Bounded Conditional Range Inversion (BCRI), which derives unbiased range estimates from reusable bounded geometric reports through an explicit local inverse. Its boundary-conditioned estimator achieves no larger expected L2 loss than the unbounded inverse, and histogram preprocessing supports constant-time queries. The same reports also provide a nonnegative, unbiased variance estimate for every answer. At the center of the framework, Adaptive Estimator Selection (AES) privately predicts bias, variance, and covariance to combine BCRI with a conditional estimator from the same transcript. Experiments on diverse real-world graph tasks demonstrate the accuracy, efficiency, and workload scalability of the proposed framework.