{"type":"ScholarlyArticle","title":"Computing Twin-width with SAT and Branch & Bound","authors":[{"name":"André Schidler","slug":"andre-schidler","given":"Andre","family":"Schidler","affiliation":"Algorithms and Complexity Group , TU Wien , Vienna , Austria"},{"name":"Stefan Szeider","slug":"stefan-szeider","given":"Stefan","family":"Szeider","affiliation":"Algorithms and Complexity Group , TU Wien , Vienna , Austria"}],"abstract":"The graph width-measure twin-width recently attracted great attention because of its solving power and generality. Many prominent NP-hard problems are tractable on graphs of bounded twin-width if a certificate for the twin-width bound is provided as an input. Bounded twin-width subsumes other prominent structural restrictions such as bounded treewidth and bounded rank-width.\r\nComputing such a  certificate is NP-hard itself, already for twin-width 4, and the only known implemented algorithm for twin-width computation is based on a SAT encoding.\r\n\r\nIn this paper, we propose two new algorithmic approaches for computing twin-width that\r\nsignificantly improve the state of the art.\r\nFirstly, we develop a SAT encoding that is far more compact than the known encoding and consequently scales to larger graphs. Secondly, we propose a new Branch & Bound algorithm for twin-width that, on many graphs, is significantly faster than the SAT encoding. It utilizes a sophisticated caching system for partial solutions.\r\nBoth algorithmic approaches are based on new conceptual insights into twin-width computation,\r\nincluding the reordering of contractions.","doi":"10.24963/ijcai.2023/224","url":"https://ijcai.org/proceedings/2023/224","pdf":"https://ijcai.org/proceedings/2023/0224.pdf","markdown":"https://ijcai.org/proceedings/2023/224.md","bibtex":"https://ijcai.org/proceedings/2023/bibtex/224","volume":{"slug":"2023","title":"Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2023","url":"https://ijcai.org/proceedings/2023/","year":2023,"location":"Macao, SAR","dates":"19-25 August 2023","editors":"Edith Elkind","isbn":"978-1-956792-03-4","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2023"},"section":"Constraint Satisfaction and Optimization","track":"Main Track","number":224,"pages":{"first":2013,"last":2021},"keywords":["Constraint Satisfaction and Optimization: CSO: Constraint programming","Constraint Satisfaction and Optimization: CSO: Applications","Constraint Satisfaction and Optimization: CSO: Constraint satisfaction"],"videos":[],"references":[{"position":1,"raw":"[Ahn et al., 2022] Jungho Ahn, Kevin Hendrey, Donggyu Kim, and Sang-il Oum. 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