Differential privacy (DP) has gained significant attention lately as the state of the art in privacy protection. It achieves privacy by adding noise to query answers. We study the problem of privately and accurately answering a set of statistical range queries in batch mode (i.e., under non-interactive DP). The noise magnitude in DP depends directly on the sensitivity of a query set, and calculating sensitivity was proven to be NP-hard. Therefore, efficiently bounding the sensitivity of a given query set is still an open research problem. In this work, we propose upper bounds on sensitivity that are tighter than those in previous work. We also propose a formulation to exactly calculate sensitivity for a set of COUNT queries. However, it is impractical to implement these bounds without sophisticated methods. We therefore introduce methods that build a graph model $G$G based on a query set $Q$Q, such that implementing the aforementioned bounds can be achieved by solving two well-known clique problems on $G$G. We make use of the literature in solving these clique problems to realize our bounds efficiently. Experimental results show that for query sets with a few hundred queries, it takes only a few seconds to obtain results.

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非交互式差分隐私的敏感性分析：边界和高效算法

差分隐私（DP）最近作为隐私保护的最新技术受到了极大的关注。它通过在查询答案中添加噪音来实现隐私。我们研究了在批处理模式下（即在非交互式 DP 下）私下准确地回答一组统计范围查询的问题。DP 中的噪声大小直接取决于查询集的敏感度，并且计算敏感度被证明是 NP-hard 的。因此，有效地限制给定查询集的敏感性仍然是一个开放的研究问题。在这项工作中，我们提出了比以前工作更严格的灵敏度上限。我们还提出了一个公式来精确计算一组 COUNT 查询的敏感度。然而，没有复杂的方法来实现这些边界是不切实际的。$G$G 基于查询集 $Q$问，这样就可以通过解决两个众所周知的派系问题来实现上述边界 $G$G. 我们利用文献解决这些集团问题来有效地实现我们的界限。实验结果表明，对于几百个查询的查询集，只需要几秒钟就可以得到结果。