Related papers: Preserving Diversity when Partitioning: A Geometri…
Stable matching theory is the foundation of centralized clearinghouses worldwide, from school choice programs to medical residency allocations. However, incorporating complex distributional goals-such as multi-dimensional diversity quotas…
Partisan gerrymandering poses a threat to democracy. Moreover, the complexity of the districting task may exceed human capacities. One potential solution is using computational models to automate the districting process by optimizing…
Symmetry is a guiding principle in physics that allows to generalize conclusions between many physical systems. In the ongoing search for new topological phases of matter, symmetry plays a crucial role because it protects topological…
The objective of clustering is to discover natural groups in datasets and to identify geometrical structures which might reside there, without assuming any prior knowledge on the characteristics of the data. The problem can be seen as…
The partition problem is a well-known basic NP-complete problem. We mainly consider the optimization version of it in this paper. The problem has been investigated from various perspectives for a long time and can be solved efficiently in…
A long line of literature has focused on the problem of selecting a team of individuals from a large pool of candidates, such that certain constraints are respected, and a given objective function is maximized. Even though extant research…
Quantification of measurement uncertainty is crucial for robust scientific inference, yet accurate estimates of this uncertainty remain elusive for ecological measures of diversity. Here, we address this longstanding challenge by deriving a…
Recent works have studied the design of algorithms for selecting representative sortition panels. However, the most central question remains unaddressed: Do these panels reflect the entire population's opinion? We present a positive answer…
We investigate a new model for partitioning a set of items into groups (clusters). The number of groups is given and the distances between items are well defined. These distances may include weights. The sum of the distances between all…
A theorem of Davies states that for symmetric quantum states there exists a symmetric POVM maximizing the mutual information. To apply this theorem the representation of the symmetry group has to be irreducible. We obtain a similar yet…
Extraction of structure, in particular of group symmetries, is increasingly crucial to understanding and building intelligent models. In particular, some information-theoretic models of parsimonious learning have been argued to induce…
Communities are ubiquitous in nature and society. Individuals that share common properties often self-organize to form communities. Avoiding the shortages of computation complexity, pre-given information and unstable results in different…
We propose a statistical framework to identify topological differences in two populations of random geometric objects. The proposed framework involves first associating a topological signature with random geometric objects and then…
We introduce two models of multiwinner elections with approval preferences and labelled candidates that take the committee's diversity into account. One model aims to find a committee with maximal diversity given a scoring function (e.g. of…
The paper presents the investigation and implementation of the relationship between diversity and the performance of multiple classifiers on classification accuracy. The study is critical as to build classifiers that are strong and can…
I survey recent progress on a classic and challenging problem in social choice: the fair division of indivisible items. I discuss how a computational perspective has provided interesting insights into and understanding of how to divide…
Community partitioning is crucial in network analysis, with modularity optimization being the prevailing technique. However, traditional modularity-based methods often overlook fairness, a critical aspect in real-world applications. To…
The characterization of network community structure has profound implications in several scientific areas. Therefore, testing the algorithms developed to establish the optimal division of a network into communities is a fundamental problem…
The persistence probability is a statistical index that has been proposed to detect one or more communities embedded in a network. Even though its definition is straightforward, e.g, the probability that a random walker remains in a group…
Population diversity is crucial in evolutionary algorithms to enable global exploration and to avoid poor performance due to premature convergence. This book chapter reviews runtime analyses that have shown benefits of population diversity,…