Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Preserving Diversity when Partitioning: A Geometric Approach   Diversity plays a crucial role in multiple contexts such as team formation,
representation of minority groups and generally when allocating resources
fairly. Given a community composed by individuals of different types, we study
the problem of partitioning this community such that the global diversity is
preserved as much as possible in each subgroup. We consider the diversity
metric introduced by Simpson in his influential work that, roughly speaking,
corresponds to the inverse probability that two individuals are from the same
type when taken uniformly at random, with replacement, from the community of
interest. We provide a novel perspective by reinterpreting this quantity in
geometric terms. We characterize the instances in which the optimal partition
exactly preserves the global diversity in each subgroup. When this is not
possible, we provide an efficient polynomial-time algorithm that outputs an
optimal partition for the problem with two types. Finally, we discuss further
challenges and open questions for the problem that considers more than two
types.

37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
2
The categories of this paper are: math
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an