Max-Min Diversification with Fairness Constraints: Exact and Approximation Algorithms
This addresses fairness in diversity maximization for applications like data summarization and recommender systems, but it is incremental as it builds on existing diversification methods by adding constraints.
The paper tackles the problem of selecting a diverse subset of items from a dataset while ensuring fairness across groups defined by sensitive attributes, proposing an exact algorithm for small datasets and a scalable approximation algorithm with a performance guarantee, and demonstrates superior results in experiments on real-world data.
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.