{"type":"ScholarlyArticle","title":"Polynomial Time Presolve Algorithms for Rotation-Based Models Solving the Robust Stable Matching Problem","authors":[{"name":"Sulian Le Bozec-Chiffoleau","slug":"sulian-le-bozec-chiffoleau","given":"Sulian","family":"Le Bozec-Chiffoleau","affiliation":"TASC , Institut Mines Telecom Atlantique , LS2N; UMR 6004 , Nantes , France"},{"name":"Charles Prud'homme","slug":"charles-prud-homme","given":"Charles","family":"Prud'homme","affiliation":"TASC , Institut Mines Telecom Atlantique , LS2N; UMR 6004 , Nantes , France"},{"name":"Gilles Simonin","slug":"gilles-simonin","given":"Gilles","family":"Simonin","affiliation":"TASC , Institut Mines Telecom Atlantique , LS2N; UMR 6004 , Nantes , France"}],"abstract":"The Robust Stable Matching (RSM) problem involves finding a stable matching that allows getting another stable matching within a minimum number of changes when a pair becomes forbidden. It has been shown that such a problem is NP-Hard. In this paper, we enrich the mathematical model for the RSM problem based on new theoretical properties. We derive from these properties new polynomial time pre-solving algorithms which both reduce the search space and speed up the exploration. We also extend our results to the instances of the Many-to-Many problem and give its corresponding constraint programming (CP) model. We show how the use of our algorithms improve the state-of-the-art results and make it possible to obtain proofs of optimality on large instances via the CP model.","doi":"10.24963/ijcai.2024/317","url":"https://ijcai.org/proceedings/2024/317","pdf":"https://ijcai.org/proceedings/2024/0317.pdf","markdown":"https://ijcai.org/proceedings/2024/317.md","bibtex":"https://ijcai.org/proceedings/2024/bibtex/317","volume":{"slug":"2024","title":"Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2024","url":"https://ijcai.org/proceedings/2024/","year":2024,"location":"Jeju, Korea","dates":"3-9 August 2024","editors":"Kate Larson","isbn":"978-1-956792-04-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2024"},"section":"Game Theory and Economic Paradigms","track":"Main Track","number":317,"pages":{"first":2860,"last":2867},"keywords":["Constraint Satisfaction and Optimization: CSO: Modeling","Knowledge Representation and Reasoning: KRR: Preference modelling and preference-based reasoning","Game Theory and Economic Paradigms: GTEP: Computational social choice","AI Ethics, Trust, Fairness: ETF: Safety and robustness"],"videos":[],"references":[{"position":1,"raw":"[Baıou and Balinski, 2000] Mourad Baıou and Michel Balinski. 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