  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.
