Related papers: Preserving Diversity when Partitioning: A Geometri…
Diversity measurement underpins the study of biological systems, but measures used vary across disciplines. Despite their common use and broad utility, no unified framework has emerged for measuring, comparing and partitioning diversity.…
The goal of group formation is to build a team to accomplish a specific task. Algorithms are employed to improve the effectiveness of the team so formed and the efficiency of the group selection process. However, there is concern that team…
Diversity is an important principle in data selection and summarization, facility location, and recommendation systems. Our work focuses on maximizing diversity in data selection, while offering fairness guarantees. In particular, we offer…
Socioeconomic segregation often arises in school districting and other contexts, causing some groups to be over- or under-represented within a particular district. This phenomenon is closely linked with disparities in opportunities and…
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…
Diversity maximization is an important geometric optimization problem with many applications in recommender systems, machine learning or search engines among others. A typical diversification problem is as follows: Given a finite metric…
This paper is about how to partition decision variables while decomposing a large-scale optimization problem for the best performance of distributed solution methods. Solving a large-scale optimization problem sequen- tially can be…
For many graph-related problems, it can be essential to have a set of structurally diverse graphs. For instance, such graphs can be used for testing graph algorithms or their neural approximations. However, to the best of our knowledge, the…
Maximum diversity aims at selecting a diverse set of high-quality objects from a collection, which is a fundamental problem and has a wide range of applications, e.g., in Web search. Diversity under a uniform or partition matroid constraint…
We model the societal task of redistricting political districts as a partitioning problem: Given a set of $n$ points in the plane, each belonging to one of two parties, and a parameter $k$, our goal is to compute a partition $\Pi$ of the…
The set of answers to a query may be very large, potentially overwhelming users when presented with the entire set. In such cases, presenting only a small subset of the answers to the user may be preferable. A natural requirement for this…
Diversity is a central concept in many fields. Despite its importance, there is no unified methodological framework to measure diversity and its three components of variety, balance and disparity. Current approaches take into account…
We consider the {\em clustering with diversity} problem: given a set of colored points in a metric space, partition them into clusters such that each cluster has at least $\ell$ points, all of which have distinct colors. We give a…
The apportionment problem constitutes a fundamental problem in democratic societies: How to distribute a fixed number of seats among a set of states in proportion to the states' populations? This--seemingly simple--task has led to a rich…
We first consider interval partitions whose complements are Lebesgue-null and introduce a complete metric that induces the same topology as the Hausdorff distance (between complements). This is done using correspondences between intervals.…
In this paper, we consider the problem of partitioning a polygon into a set of connected disjoint sub-polygons, each of which covers an area of a specific size. The work is motivated by terrain covering applications in robotics, where the…
Understanding the role of demographic diversity in group settings requires effective quantitative metrics. Intersectional feminist theory has highlighted that demographic identities can intersect in complex ways, but most metrics used to…
We study the probabilistic assignment of items to platforms that satisfies both group and individual fairness constraints. Each item belongs to specific groups and has a preference ordering over platforms. Each platform enforces group…
Diversity can be broadly defined as the presence of meaningful variation across elements, which can be viewed from multiple perspectives, including statistical variation and geometric structural richness in the dataset. Existing diversity…
Multilevel selection and the evolution of cooperation are fundamental to the formation of higher-level organisation and the evolution of biocomplexity, but such notions are controversial and poorly understood in natural populations. The…