{"type":"ScholarlyArticle","title":"Stable Matchings with Diversity Constraints: Affirmative Action is beyond NP","authors":[{"name":"Jiehua Chen","slug":"jiehua-chen","given":"Jiehua","family":"Chen","affiliation":"TU Wien , Vienna , Austria"},{"name":"Robert Ganian","slug":"robert-ganian","given":"Robert","family":"Ganian","affiliation":"TU Wien , Vienna , Austria"},{"name":"Thekla Hamm","slug":"thekla-hamm","given":"Thekla","family":"Hamm","affiliation":"TU Wien , Vienna , Austria"}],"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? \r\n\r\nSMTI-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 Σ^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.","doi":"10.24963/ijcai.2020/21","url":"https://ijcai.org/proceedings/2020/21","pdf":"https://ijcai.org/proceedings/2020/0021.pdf","markdown":"https://ijcai.org/proceedings/2020/21.md","bibtex":"https://ijcai.org/proceedings/2020/bibtex/21","volume":{"slug":"2020","title":"Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2020","url":"https://ijcai.org/proceedings/2020/","year":2020,"location":"Yokohama","dates":"January 2021 (postponed from 11-17 July 2020)","editors":"Christian Bessiere","isbn":"978-0-9992411-6-5","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2020"},"section":"Agent-based and Multi-agent Systems","track":"Main track","number":21,"pages":{"first":146,"last":152},"keywords":["Agent-based and Multi-agent Systems: Algorithmic Game Theory","Agent-based and Multi-agent Systems: Computational Social Choice","Agent-based and Multi-agent Systems: Economic Paradigms, Auctions and Market-Based Systems"],"videos":[{"label":"Video","url":"https://videos.ijcai20.org/26571/file_26571.m3u8","length_sec":850,"provider":"hls"}],"references":[{"position":1,"raw":"[Abdulkadiroǧlu, 2005] Atila Abdulkadiroǧlu. 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