Multi-Attribute Group Fairness in $k$-NN Queries on Vector Databases

TL;DR

This paper introduces a framework for multi-attribute group fairness in $k$-NN searches on vector databases, balancing fairness constraints with search efficiency and proposing algorithms for exact and approximate solutions.

Contribution

It develops a novel computational framework that enforces multi-attribute fairness constraints in $k$-NN search, including algorithms for exact and approximate solutions with theoretical guarantees.

Findings

The framework effectively balances fairness, search time, and memory.

Locality-sensitive hashing accelerates candidate generation under fairness constraints.

Experimental results show scalability and generality of the approach.

Abstract

We initiate the study of multi-attribute group fairness in $k$-nearest neighbor ($k$-NN) search over vector databases. Unlike prior work that optimizes efficiency or query filtering, fairness imposes count constraints to ensure proportional representation across groups defined by protected attributes. When fairness spans multiple attributes, these constraints must be satisfied simultaneously, making the problem computationally hard. To address this, we propose a computational framework that produces high-quality approximate nearest neighbors with good trade-offs between search time, memory/indexing cost, and recall. We adapt locality-sensitive hashing (LSH) to accelerate candidate generation and build a lightweight index over the Cartesian product of protected attribute values. Our framework retrieves candidates satisfying joint count constraints and then applies a post-processing stage to construct fair $k$-NN results across all attributes. For 2 attributes, we present an exact polynomial-time flow-based algorithm; for 3 or more, we formulate ILP-based exact solutions with higher computational cost. We provide theoretical guarantees, identify efficiency--fairness trade-offs, and empirically show that existing vector search methods cannot be directly adapted for fairness. Experimental evaluations demonstrate the generality of the proposed framework and scalability.