AI 中文总结
针对现有OLH模拟复杂度高的问题，提出2-Binom和3-Binom两种基于二项式建模的快速算法，将复杂度降至$O(n+d)$，在保持统计等价性的同时大幅缩短执行时间。
AI 中文摘要
优化局部哈希（OLH）是一种广泛应用的基于哈希的局部差分隐私（LDP）协议，而基于模拟的实验是研究中评估OLH及基于OLH的应用的标准方法。然而，现有OLH模拟的计算复杂度为$O(nd)$，其中$n$为用户群体规模，$d$为域大小，随着$n$和$d$的增长，会导致执行时间显著增加。本文提出两种基于二项式建模的OLH快速模拟算法（2-Binom和3-Binom），核心见解是：对于任意域值$v$，其扰动报告支持$v$的用户总数可分解为两个或三个二项式随机变量的和。利用该见解，我们的算法将模拟复杂度降至$O(n + d)$，且不损害统计等价性。特别地，我们从理论上证明，两种算法均能产生无偏频率估计，其方差与原始OLH模拟的方差完全相同。在真实世界数据集上的实验证实，两种方法均能将执行时间从数分钟缩短至毫秒级，在效用无变化的情况下实现了显著加速。
英文摘要
Optimized Local Hashing (OLH) is a widely used hash-based Local Differential Privacy (LDP) protocol, and simulation-based experimentation is the standard approach for evaluating OLH and OLH-based applications in research. However, the existing OLH simulations have $O(nd)$ computational complexity, where $n$ is the user population size and $d$ is the domain size, and can lead to significant execution times as $n$ and $d$ grow. In this paper, we propose two fast simulation algorithms for OLH (2-Binom and 3-Binom) grounded in Binomial modeling. Our key insight is that, for any domain value $v$, the total number of users whose perturbed reports support $v$ can be decomposed into a sum of two or three Binomial random variables. Using this insight, our algorithms reduce the simulation complexity to $O(n + d)$ without hurting statistical equivalence. In particular, we theoretically prove that both algorithms yield unbiased frequency estimations with variances identical to those of the original OLH simulations. Experiments on real-world datasets confirm that both approaches reduce execution times from several minutes to milliseconds, yielding significant speedups with no change in utility.
