Target-Stratified Fair Range Summaries: Improved Fair $\varepsilon$-Nets and Geometric Hitting Sets

2026-09-17

AI Summary

该研究通过目标分层抽样方法解决了ε-网和几何打击集的公平性问题，改进了在保持范围有效性的同时控制组构成的方法，适用于人口均衡与自定义比例目标。

Abstract

Compact summaries are a key tool for approximate query processing over large datasets. For range-query workloads, an $\varepsilon$-net provides a small summary that hits every sufficiently large range. However, classical $\varepsilon$-nets only guarantee range validity and do not control the group composition of the selected tuples. As a result, the summary may be range-valid but poorly representative, which can propagate imbalance to downstream query results. Motivated by recent work on fair $\varepsilon$-nets and fair geometric hitting sets \cite{dehghankar2025fair}, we study fairness-aware range summaries under prescribed target group ratios. Different from previous sample-and-repair approach, we propose a target-stratified sampling method. For demographic parity (in which the ratio of fairness is determined by group proportion), our sample size is $O(A_{\varepsilon})$, coinciding with the standard $\varepsilon$-net bound, improving previous bound of $O\!\left(A_\varepsilon\log\frac{k}{\varphi}\right)$. For custom-ratio targets (in which the ratio of fairness is determined by manually defined proportion), our sample size is $O(A_Γ)$, where $Γ$ is a parameter measuring the gap between the customized ratio and the demographic parity; we prove that this dependence on $Γ$ is unavoidable, with a worst-case lower bound of $Ω(Γ/\varepsilon)$. Using our target-stratified sampling method, we could improve the previous approximation ratio for the fair geometric hitting set problem by a logarithmic factor, and making use of this result, we could in turn improve the size of custom-ratio fair $\varepsilon$-net. Experiments on real and synthetic datasets demonstrate that our method constructs smaller fair summaries than existing approaches, scales to large datasets and fine-grained group constraints, and improves downstream range query processing.

Problem

• fairness
• range summaries
• ε-net
• geometric hitting sets
• demographic parity

Innovation

• target-stratified sampling
• fair ε-nets
• geometric hitting sets
• demographic parity
• custom-ratio fairness