# PriPL-Tree: Accurate Range Query for Arbitrary Distribution under Local Differential Privacy

arXiv: https://arxiv.org/abs/2407.13532 · HTML: https://mlsanity.com/paper/2407.13532/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jul 2024.

## Built on by (most cited first, 1 of 1)

- [Data Poisoning Attacks to Locally Differentially Private Range Query Protocols](https://mlsanity.com/paper/2503.03454/) (2025)

## Abstract (arXiv)

Answering range queries in the context of Local Differential Privacy (LDP) is a widely studied problem in Online Analytical Processing (OLAP). Existing LDP solutions all assume a uniform data distribution within each domain partition, which may not align with real-world scenarios where data distribution is varied, resulting in inaccurate estimates. To address this problem, we introduce PriPL-Tree, a novel data structure that combines hierarchical tree structures with piecewise linear (PL) functions to answer range queries for arbitrary distributions. PriPL-Tree precisely models the underlying data distribution with a few line segments, leading to more accurate results for range queries. Furthermore, we extend it to multi-dimensional cases with novel data-aware adaptive grids. These grids leverage the insights from marginal distributions obtained through PriPL-Trees to partition the grids adaptively, adapting the density of underlying distributions. Our extensive experiments on both real and synthetic datasets demonstrate the effectiveness and superiority of PriPL-Tree over state-of-the-art solutions in answering range queries across arbitrary data distributions.