Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stable Matchings with Diversity Constraints: Affirmative Action is
  beyond NP   We investigate the following many-to-one stable matching problem with
diversity constraints (SMTI-Diverse): Given a set of students and a set of
colleges which have preferences over each other, where the students have
overlapping types, and the colleges each have a total capacity as well as
quotas for individual types (the diversity constraints), is there a matching
satisfying all diversity constraints such that no unmatched student-college
pair has an incentive to deviate?
  SMTI-Diverse is known to be NP-hard. However, as opposed to the NP-membership
claims in the literature [Aziz et al., AAMAS 2019; Huang, SODA 2010], we prove
that it is beyond NP: it is complete for the complexity class
$\Sigma^{\text{P}}_2$. In addition, we provide a comprehensive analysis of the
problem's complexity from the viewpoint of natural restrictions to inputs and
obtain new algorithms for the problem.

12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an