{"type":"ScholarlyArticle","title":"DoubleLex Revisited and Beyond","authors":[{"name":"Xuming Huang","slug":"xuming-huang","given":"Xuming","family":"Huang","affiliation":"Department of Computer Science and Engineering , The Chinese University of Hong Kong Shatin , N.T. , Hong Kong"},{"name":"Jimmy Lee","slug":"jimmy-lee","given":"Jimmy","family":"Lee","affiliation":"Department of Computer Science and Engineering , The Chinese University of Hong Kong Shatin , N.T. , Hong Kong"}],"abstract":"The paper proposes Maximum Residue (MR) as a notion to evaluate the strength of a symmetry breaking method.  We give a proof to improve the best known DoubleLex MR upper bound from m!n! - (m!+n!) to min(m!,n!) for an m x n matrix model. Our result implies that DoubleLex works well on matrix models where min(m, n) is relatively small. We further study the MR bounds of SwapNext and SwapAny, which are extensions to DoubleLex breaking further a small number of composition symmetries. Such theoretical comparisons suggest general principles on selecting Lex-based symmetry breaking methods based on the dimensions of the matrix models. Our experiments confirm the theoretical predictions as well as efficiency of these methods.","doi":"10.24963/ijcai.2019/154","url":"https://ijcai.org/proceedings/2019/154","pdf":"https://ijcai.org/proceedings/2019/0154.pdf","markdown":"https://ijcai.org/proceedings/2019/154.md","bibtex":"https://ijcai.org/proceedings/2019/bibtex/154","volume":{"slug":"2019","title":"Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2019","url":"https://ijcai.org/proceedings/2019/","year":2019,"location":"Macao","dates":"10-16 August 2019","editors":"Sarit Kraus","isbn":"978-0-9992411-4-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2019"},"section":"Constraints and SAT","track":"Main track","number":154,"pages":{"first":1101,"last":1107},"keywords":["Constraints and SAT: Constraint Satisfaction","Constraints and SAT: Modeling;Formulation"],"videos":[],"references":[{"position":1,"raw":"[Flener et al., 2001] Pierre Flener, Alan M. 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