Local differential privacy (LDP) has recently emerged as a popular privacy standard. With the growing popularity of LDP, several recent works have applied LDP to spatial data, and grid-based decompositions have been a common building block in the collection and analysis of spatial data under DP and LDP. In this paper, we study three grid-based decomposition methods for spatial data under LDP: Uniform Grid (UG), PrivAG, and AAG. UG is a static approach that consists of equal-sized cells. To enable data-dependent decomposition, PrivAG was proposed by Yang et al. as the most recent adaptive grid method. To advance the state-of-the-art in adaptive grids, in this paper we propose the Advanced Adaptive Grid (AAG) method. For each grid cell, following the intuition that the cell's intra-cell density distribution will be affected by its neighbors, AAG performs uneven cell divisions depending on the neighboring cells' densities. We experimentally compare UG, PrivAG, and AAG using three real-world location datasets, varying privacy budgets, and query sizes. Results show that AAG provides higher utility than PrivAG, demonstrating the superiority of our proposed approach. Furthermore, UG's performance is heavily dependent on the choice of grid size. When the grid size is chosen optimally in UG, AAG still beats UG for small queries, but UG beats AAG for large (coarse-grained) queries.

翻译：本地差分隐私（LDP）近年来已成为一种主流的隐私保护标准。随着LDP的普及，近期多项研究将其应用于空间数据领域，而基于网格的分解方法已成为差分隐私（DP）和LDP框架下空间数据采集与分析的通用基础模块。本文系统研究了LDP环境下三种基于网格的空间数据分解方法：均匀网格（UG）、PrivAG与AAG。UG作为一种静态方法，采用等尺寸网格单元划分。为实现数据自适应的分解，Yang等人提出了当前最新的自适应网格方法PrivAG。为推进自适应网格技术的进展，本文提出高级自适应网格（AAG）方法。该方法基于"网格单元内部密度分布受相邻单元影响"的洞见，针对每个网格单元，依据相邻单元的密度分布进行非均匀的单元划分。我们通过三组真实世界位置数据集，在不同隐私预算和查询规模的设定下，对UG、PrivAG和AAG进行了实验比较。结果表明，AAG在数据效用性方面优于PrivAG，验证了所提方法的优越性。此外，UG的性能高度依赖于网格尺寸的选择：即使在UG采用最优网格尺寸的情况下，AAG在小规模查询中仍优于UG，而UG在大型（粗粒度）查询中表现更佳。