Stable matchings with diversity constraints: Affirmative action is beyond NP

Jiehua Chen, Robert Ganian, Thekla Hamm

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

Abstract

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., 2019; Huang, 2010], we prove that it is beyond NP: it is complete for the complexity class SP2. 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.

Original languageEnglish
Title of host publicationProceedings of the 29th International Joint Conference on Artificial Intelligence, IJCAI 2020
EditorsChristian Bessiere
PublisherInternational Joint Conferences on Artificial Intelligence
Pages146-152
Number of pages7
ISBN (Electronic)9780999241165
StatePublished - 1 Jan 2020
Externally publishedYes
Event29th International Joint Conference on Artificial Intelligence, IJCAI 2020 - Yokohama, Japan
Duration: 1 Jan 2021 → …

Publication series

NameIJCAI International Joint Conference on Artificial Intelligence
Volume2021-January
ISSN (Print)1045-0823

Conference

Conference29th International Joint Conference on Artificial Intelligence, IJCAI 2020
Country/TerritoryJapan
CityYokohama
Period1/01/21 → …

ASJC Scopus subject areas

  • Artificial Intelligence

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