Max-Min Diversification with Fairness Constraints: Exact and Approximation Algorithms

TL;DR

This paper introduces algorithms for fair diversity maximization that balance representativeness with fairness constraints, providing exact solutions for small datasets and scalable approximations for larger ones.

Contribution

It presents an exact integer linear programming approach and a scalable approximation algorithm for max-min diversification with fairness constraints, addressing fairness issues in diversity maximization.

Findings

Exact ILP algorithm effective on small datasets

Approximation algorithm scalable to large datasets

Algorithms outperform existing methods in experiments

Abstract

Diversity maximization aims to select a diverse and representative subset of items from a large dataset. It is a fundamental optimization task that finds applications in data summarization, feature selection, web search, recommender systems, and elsewhere. However, in a setting where data items are associated with different groups according to sensitive attributes like sex or race, it is possible that algorithmic solutions for this task, if left unchecked, will under- or over-represent some of the groups. Therefore, we are motivated to address the problem of \emph{max-min diversification with fairness constraints}, aiming to select $k$ items to maximize the minimum distance between any pair of selected items while ensuring that the number of items selected from each group falls within predefined lower and upper bounds. In this work, we propose an exact algorithm based on integer linear programming that is suitable for small datasets as well as a $\frac{1-\varepsilon}{5}$-approximation algorithm for any $\varepsilon \in (0, 1)$ that scales to large datasets. Extensive experiments on real-world datasets demonstrate the superior performance of our proposed algorithms over existing ones.