Fair Diversity Maximization with Few Representatives

TL;DR

This paper introduces a randomized algorithm for fair diversity maximization that improves approximation ratios, especially when selecting few representatives per group, and demonstrates its effectiveness on large datasets.

Contribution

The paper presents a novel randomized algorithm with improved approximation guarantees for fair diversity maximization with few representatives, using padded decompositions and clustering techniques.

Findings

Improved approximation ratio of .5f3(\u00b5) for the problem.

Algorithm effectively handles large datasets with fair representation constraints.

Experimental results confirm the algorithm's practical efficiency.

Abstract

Diversity maximization problem is a well-studied problem where the goal is to find $k$ diverse items. Fair diversity maximization aims to select a diverse subset of $k$ items from a large dataset, while requiring that each group of items be well represented in the output. More formally, given a set of items with labels, our goal is to find $k$ items that maximize the minimum pairwise distance in the set, while maintaining that each label is represented within some budget. In many cases, one is only interested in selecting a handful (say a constant) number of items from each group. In such scenario we show that a randomized algorithm based on padded decompositions improves the state-of-the-art approximation ratio to $\sqrt{\log(m)}/(3m)$, where $m$ is the number of labels. The algorithms work in several stages: ($i$) a preprocessing pruning which ensures that points with the same label are far away from each other, ($ii$) a decomposition phase, where points are randomly placed in clusters such that there is a feasible solution with maximum one point per cluster and that any feasible solution will be diverse, $(iii)$ assignment phase, where clusters are assigned to labels, and a representative point with the corresponding label is selected from each cluster. We experimentally verify the effectiveness of our algorithm on large datasets.